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Local polynomial prediction method of multivariate chaotic time series and its application 认领 引用 被引量：3
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作者 方芬 王海燕 《Journal of Southeast University(English Edition)》 EI CAS 2005年第2期229-232,共4页
To improve the prediction accuracy of chaotic time series, a new methodformed on the basis of local polynomial prediction is proposed. The multivariate phase spacereconstruction theory is utilized to reconstruct the p... To improve the prediction accuracy of chaotic time series, a new methodformed on the basis of local polynomial prediction is proposed. The multivariate phase spacereconstruction theory is utilized to reconstruct the phase space firstly, and on its basis, apolynomial function is applied to construct the prediction model, then the parameters of the modelaccording to the data matrix built with the embedding dimensions are estimated and a one-stepprediction value is calculated. An estimate and one-step prediction value is calculated. Finally,the mean squared root statistics are used to estimate the prediction effect. The simulation resultsobtained by the Lorenz system and the prediction results of the Shanghai composite index show thatthe local polynomial prediction errors of the multivariate chaotic time series are small and itsprediction accuracy is much higher than that of the univariate chaotic time series. 展开更多
关键词 chaotic time series phase space reconstruction local polynomial prediction stock market
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Application of local polynomial estimation in suppressing strong chaotic noise 认领 引用 被引量：7
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作者 Su Li-Yun Ma Yan-Ju Li Jiao-Jun 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第2期181-186,共6页
In this paper, we propose a new method that combines chaotic series phase space reconstruction and local polynomial estimation to solve the problem of suppressing strong chaotic noise. First, chaotic noise time series... In this paper, we propose a new method that combines chaotic series phase space reconstruction and local polynomial estimation to solve the problem of suppressing strong chaotic noise. First, chaotic noise time series are reconstructed to obtain multivariate time series according to Takens delay embedding theorem. Then the chaotic noise is estimated accurately using local polynomial estimation method. After chaotic noise is separated from observation signal, we can get the estimation of the useful signal. This local polynomial estimation method can combine the advantages of local and global law. Finally, it makes the estimation more exactly and we can calculate the formula of mean square error theoretically. The simulation results show that the method is effective for the suppression of strong chaotic noise when the signal to interference ratio is low. 展开更多
关键词 strong chaotic noise local polynomial estimation weak signal detection
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Local Polynomial Estimation of Distribution Functions 认领 引用
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作者 李永红 曾霞 《Journal of Southwest Jiaotong University(English Edition)》 2007年第1期65-69,共5页
Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate ... Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate of strong convergence of the estimations. 展开更多
关键词 Local polynomial method Strong consistency Hazard function
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Local Polynomial Regression Estimator of the Finite Population Total under Stratified Random Sampling: A Model-Based Approach 认领 引用
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作者 Charles K. Syengo Sarah Pyeye +1 位作者 George O. Orwa Romanus O. Odhiambo 《Open Journal of Statistics》 2016年第6期1085-1097,共13页
In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by ... In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by making use of the local polynomial regression estimation to predict the nonsampled values of the survey variable y. The performance of the proposed estimator is investigated against some design-based and model-based regression estimators. The simulation experiments show that the resulting estimator exhibits good properties. Generally, good confidence intervals are seen for the nonparametric regression estimators, and use of the proposed estimator leads to relatively smaller values of RE compared to other estimators. 展开更多
关键词 Sample Surveys Stratified Random Sampling Auxiliary Information Local Polynomial Regression Model-Based Approach Nonparametric Regression
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Weighted local polynomial estimations of a non-parametric function with censoring indicators missing at random and their applications 认领 引用
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作者 Jiangfeng WANG Yangcheng ZHOU Ju TANG 《Frontiers of Mathematics in China》 SCIE CSCD 2022年第1期117-139,共23页
In this paper,we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random... In this paper,we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random,and establish the asymptotic normality of these estimators.As their applications,we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function,the conditional density function and the conditional quantile function,and investigate the asymptotic normality of these estimators.Finally,the simulation studies are conducted to illustrate the finite sample performance of the estimators. 展开更多
关键词 Local polynomial estimation asymptotic normality non-parametric function censoring indicator missing at random
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Local Polynomial-Brunk Estimation in Semi-Parametric Monotone Errors-in-Variables Model with Right-Censored Data 认领 引用 被引量：1
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作者 XIA Wei CHEN Zhao +1 位作者 WU Wuqing ZHOU Jianjun 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2015年第4期938-960,共23页
This paper introduces a semi-parametric model with right-censored data and a monotone constraint on the nonparametrie part. The authors study the local linear estimators of the parametric coefficients and apply B-spli... This paper introduces a semi-parametric model with right-censored data and a monotone constraint on the nonparametrie part. The authors study the local linear estimators of the parametric coefficients and apply B-spline method to approximate the nonparametric part based on grouped data. The authors obtain the rates of convergence for parametric and nonparametric estimators. Moreover, the authors also prove that the nonparametric estimator is consistent at the boundary. At last, the authors investigate the finite sample performance of the estimation. 展开更多
关键词 B-spline grouped brunk local polynomial monotone regression right-censored semi-parametric model.
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LOCAL POLYNOMIAL DOUBLE-SMOOTHING ESTIMATION OF A CONDITIONAL DISTRIBUTION FUNCTION WITH DEPENDENT 认领 引用
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作者 Mimi Hong Xianzhu Xiong 《Annals of Applied Mathematics》 2017年第4期364-378,共15页
Based on the idea of local polynomial double-smoother, we propose an estimator of a conditional cumulative distribution function with dependent and left-truncated data. It is assumed that the observations form a stati... Based on the idea of local polynomial double-smoother, we propose an estimator of a conditional cumulative distribution function with dependent and left-truncated data. It is assumed that the observations form a stationary a-mixing sequence. Asymptotic normality of the estimator is established. The finite sample behavior of the estimator is investigated via simulations. 展开更多
关键词 local polynomial double-smoother conditional cumulative distribution function left-truncated data a-mixing asymototic normality
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Moult intensity constraints along the complete moult sequence of the House Sparrow(Passer domesticus) 认领 引用 被引量：2
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作者 Santi Guallar Javier Quesada 《Avian Research》 SCIE CSCD 2023年第3期394-404,共11页
Sequence and intensity are two essential components of bird moult.While the moult sequences of remex tracts are highly homogenous across passerines,other tracts apparently show a high variability.Moreover,order of mou... Sequence and intensity are two essential components of bird moult.While the moult sequences of remex tracts are highly homogenous across passerines,other tracts apparently show a high variability.Moreover,order of moult activation among tracts are insufficiently known.Likewise,dynamics of moult intensity as moult progresses remains poorly known.Here,we provide detailed quantitative description of moult sequence and intensity in the House Sparrow(Passer domesticus).To understand their role,we tested two hypotheses on the:1) protection function of moult sequence,and 2) aerodynamic and physiological constraints on moult intensity.We scored percentage growth of 313 captured sparrows using the mass of the feathers of each tract(also length for remiges)to monitor moult intensity throughout the complete moult progress,which is defined as the fraction of new and growing feathers in a moulting bird relative to the total plumage.Moult sequence was highly variable both within wing coverts and among feather tracts,with moult sequence differing among all birds to some degree.We only found support for the protection function between greater coverts and both tertials and secondaries.Remex-moult intensity conformed to theoretical predictions,therefore lending support to the aerodynamic-constraint hypothesis.Furthermore,remex-moult speed plateaued during the central stages of moult progress.However,overall plumage-moult speed did not fit predictions of the physiological-constraint hypothesis,showing that the remex moult is only constrained by aerodynamics.Our results indicate that aerodynamic loss is not simply the inevitable effect of moult,but that moult is finely regulated to reduce aerodynamic loss.We propose that the moult of the House Sparrow is controlled through sequence and intensity adjustments in order to:1) avoid body and wing growth peaks;2) fulfil the protection function between some key feather tracts;3) reduce detrimental effects on flight ability;4) keep remex sequence fixed;and 5) relax remex replacement to last the whole moult duration. 展开更多
关键词 Functional constraints Local polynomial regression Passerine moult Physiological constraints Raggedness
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Simulated annealing algorithm for detecting graph isomorphism 认领 引用 被引量：4
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作者 Geng Xiutang Zhang Kai 《Journal of Systems Engineering and Electronics》 SCIE EI 2008年第5期1047-1052,共6页
Evolutionary computation techniques have mostly been used to solve various optimization problems,and it is well known that graph isomorphism problem(GIP)is a nondeterministic polynomial problem.A simulated annealing(S... Evolutionary computation techniques have mostly been used to solve various optimization problems,and it is well known that graph isomorphism problem(GIP)is a nondeterministic polynomial problem.A simulated annealing(SA)algorithm for detecting graph isomorphism is proposed,and the proposed SA algorithm is well suited to deal with random graphs with large size.To verify the validity of the proposed SA algorithm,simulations are performed on three pairs of small graphs and four pairs of large random graphs with edge densities 0.5,0.1,and 0.01,respectively.The simulation results show that the proposed SA algorithm can detect graph isomorphism with a high probability. 展开更多
关键词 graph isomorphism problem simulated annealing algorithm nondeterministic polynomial problem,local search.
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An invariant interest point detector under image affine transformation 认领 引用 被引量：2
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作者 林睿 黄海波 +1 位作者 孙荣川 孙立宁 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第3期914-921,共8页
For vision-based mobile robot navigation, images of the same scene may undergo a general affine transformation in the case of significant viewpoint changes. So, a novel method for detecting affine invariant interest p... For vision-based mobile robot navigation, images of the same scene may undergo a general affine transformation in the case of significant viewpoint changes. So, a novel method for detecting affine invariant interest points is proposed to obtain the invariant local features, which is coined polynomial local orientation tensor(PLOT). The new detector is based on image local orientation tensor that is constructed from the polynomial expansion of image signal. Firstly, the properties of local orientation tensor of PLOT are analyzed, and a suitable tuning parameter of local orientation tensor is chosen so as to extract invariant features. The initial interest points are detected by local maxima search for the smaller eigenvalues of the orientation tensor. Then, an iterative procedure is used to allow the initial interest points to converge to affine invariant interest points and regions. The performances of this detector are evaluated on the repeatability criteria and recall versus 1-precision graphs, and then are compared with other existing approaches. Experimental results for PLOT show strong performance under affine transformation in the real-world conditions. 展开更多
关键词 local orientation tensor interest point detector affine invariant image polynomial expansion
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Estimation of Finite Population Totals in High Dimensional Spaces 认领 引用
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作者 Festus A. Were George O. Orwa Romanus O. Otieno 《Open Journal of Statistics》 2022年第5期581-596,共16页
In this paper, the problem of Nonparametric Estimation of Finite Population Totals in high dimensional datasets is considered. A robust estimator of the Finite Population Total based on Feedforward Backpropagation Neu... In this paper, the problem of Nonparametric Estimation of Finite Population Totals in high dimensional datasets is considered. A robust estimator of the Finite Population Total based on Feedforward Backpropagation Neural Network is derived with the aid of a Super-Population Model. This current study is motivated by the fact that Local Polynomials and Kernel methods have in preceding related studies, been shown to provide good estimators for Finite Population Totals but in low dimensions. Even in these situations however, bias at boundary points presents a big challenge when using these estimators in estimating Finite Population parameters. The challenge worsens as the dimension of regressors increase. This is because as the dimension of the Regressor Vectors grows, the Sparseness of the Regressors’ values in the design space becomes unfeasible, resulting in a decrease in the fastest achievable rates of convergence of the Regression Function Estimators towards the target curve, rendering Kernel Methods and Local Polynomials ineffective to address these challenges. This study considers the technique of Artificial Neural Networks which yields robust estimators in high dimensions and reduces the estimation bias with marginal increase in variance. This is due to its Multi-Layer Structure, which can approximate a wide range of functions to any required level of precision. The estimator’s properties are developed, and a comparison with existing estimators was conducted to evaluate the estimator’s performance using real data sets acquired from the United Nations Development Programme 2020. The estimation approach performs well in an example using data from a United Nations Development Programme 2020 on the study of Human Development Index against other factors. The theoretical and practical results imply that the Neural Network estimator is highly recommended for survey sampling estimation of the finite population total. 展开更多
关键词 Neural Networks Kernel Smoother Local Polynomial Nonparametric
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Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model 认领 引用
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作者 Hui Li Zhiqiang Cao 《Open Journal of Endocrine and Metabolic Diseases》 2023年第4期514-533,共20页
Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressiv... Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model. 展开更多
关键词 Regression and Autoregressive Time Series Partial Time-Varying Coefficient Local Polynomial
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Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model 认领 引用
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作者 Hui Li Zhiqiang Cao 《Open Journal of Statistics》 2023年第4期514-533,共20页
Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressiv... Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model. 展开更多
关键词 Regression and Autoregressive Time Series Partial Time-Varying Coefficient Local Polynomial
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A Note on the Nonparametric Least-squares Test for Checking a Polynomial Relationship 认领 引用 被引量：3
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作者 Chang-lin Mei, Shu-yuan He, Yan-hua WangLMAM, Institute of Mathematics, Peking University, Beijing 100871, China School of Sciences, Xi’an Jiaotong University, Xi’an 710049, China 《Acta Mathematicae Applicatae Sinica》 2003年第3期511-520,共10页
Recently, Gijbels and Rousson[6] suggested a new approach, called nonparametric least-squares test, to check polynomial regression relationships. Although this test procedure is not only simple but also powerful in mo... Recently, Gijbels and Rousson[6] suggested a new approach, called nonparametric least-squares test, to check polynomial regression relationships. Although this test procedure is not only simple but also powerful in most cases, there are several other parameters to be chosen in addition to the kernel and bandwidth. As shown in their paper, choice of these parameters is crucial but sometimes intractable. We propose in this paper a new statistic which is based on sample variance of the locally estimated pth derivative of the regression function at each design point. The resulting test is still simple but includes no extra parameters to be determined besides the kernel and bandwidth that are necessary for nonparametric smoothing techniques. Comparison by simulations demonstrates that our test performs as well as or even better than Gijbels and Rousson’s approach. Furthermore, a real-life data set is analyzed by our method and the results obtained are satisfactory. 展开更多
关键词 Local polynomial fitting polynomial regression derivative estimation p-value
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Two-stage Local Walsh Average Estimation of Generalized Varying Coefficient Models 认领 引用
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作者 Neng-Hui ZHU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2015年第3期623-642,共20页
In this paper we investigate the robust estimation of generalized varying coefficient models in which the unknown regression coefficients may change with different explanatory variables. Based on the B-spline series a... In this paper we investigate the robust estimation of generalized varying coefficient models in which the unknown regression coefficients may change with different explanatory variables. Based on the B-spline series approximation and Walsh-average technique we develop an initial estimator for the unknown regression coefficient functions. By virtue of the initial estimator, the generalized varying coefficient model is reduced to a univariate nonparametric regression model. Then combining the local linear smooth and Walsh average technique we further propose a two-stage local linear Walsh-average estimator for the unknown regression coefficient functions. Under mild assumptions, we establish the large sample theory of the proposed estimators by utilizing the results of U-statistics and shows that the two-stage local linear Walsh-average estimator own an oracle property, namely the asymptotic normality of the two-stage local linear Walsh-average estimator of each coefficient function is not affected by other unknown coefficient functions. Extensive simulation studies are conducted to assess the finite sample performance, and a real example is analyzed to illustrate the proposed method. 展开更多
关键词 generalized varying coefficient regression Walsh-average B-spline approximation local polynomial two-stage method
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Local generalized empirical estimation of regression 认领 引用
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作者 Doksum Kjell 《Science China Mathematics》 2004年第1期114-127,共14页
Letf(x) be the density of a design variableX andm(x) = E[Y∣X = x] the regression function. Thenm(x) = G(x)/f(x), whereG(x) = rn(x)f(x). The Dirac δ-function is used to define a generalized empirical functionG n(x) f... Letf(x) be the density of a design variableX andm(x) = E[Y∣X = x] the regression function. Thenm(x) = G(x)/f(x), whereG(x) = rn(x)f(x). The Dirac δ-function is used to define a generalized empirical functionG n(x) forG(x) whose expectation equalsG(x). This generalized empirical function exists only in the space of Schwartz distributions, so we introduce a local polynomial of orderp approximation toG n(.) which provides estimators of the functionG(x) and its derivatives. The densityf(x) can be estimated in a similar manner. The resulting local generalized empirical estimator (LGE ) ofm(x) is exactly the Nadaraya-Watson estimator at interior points whenp = 1, but on the boundary the estimator automatically corrects the boundary effect. Asymptotic normality of the estimator is established. Asymptotic expressions for the mean squared errors are obtained and used in bandwidth selection. Boundary behavior of the estimators is investigated in details. We use Monte Carlo simulations to show that the proposed estimator withp = 1 compares favorably with the Nadaraya-Watson and the popular local linear regression smoother. 展开更多
关键词 boundary adaptive Dirac 5-function local polynomial local empirical Nadaraya-Watson estimator
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Polynomial Entropy of Amenable Group Actions for Noncompact Sets 认领 引用
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作者 Lei LIU Xiao Yao ZHOU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2023年第7期1351-1368,共18页
In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability measure on a compact metric space,and investigate the relation betw... In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability measure on a compact metric space,and investigate the relation between local measure-theoretic polynomial entropy of Borel probability measures and polynomial entropy on an arbitrary subset. Also, we establish a variational principle for polynomial entropy on compact subsets in the context of amenable group actions. 展开更多
关键词 Bowen polynomial entropy local measure-theoretic polynomial entropy variational principle amenable group
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A survey on the local refinable splines 认领 引用 被引量：4
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作者 LI Xin CHEN FaLai +1 位作者 KANG HongMei DENG JianSong 《Science China Mathematics》 SCIE CSCD 2016年第4期617-644,共28页
This paper provides a survey of local refinable splines,including hierarchical B-splines,T-splines,polynomial splines over T-meshes,etc.,with a view to applications in geometric modeling and iso-geometric analysis.We ... This paper provides a survey of local refinable splines,including hierarchical B-splines,T-splines,polynomial splines over T-meshes,etc.,with a view to applications in geometric modeling and iso-geometric analysis.We will identify the strengths and weaknesses of these methods and also offer suggestions for their using in geometric modeling and iso-geometric analysis. 展开更多
关键词 geometric modeling isogeometric analysis B-splines hierarchical B-splines T-splines polynomial splines over hierarchical T-meshes（PHT-splines） locally refined（LR）B-splines local refinement
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ESTIMATION ON SEMIVARYING COEFFICIENT MODELS WITH DIFFERENT DEGREES OF SMOOTHNESS 认领 引用 被引量：1
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作者 Riquan ZHANG Jingyan FENG +1 位作者 Kaichun WEN Jianhua DING 《Journal of Systems Science & Complexity》 SCIE EI 2009年第3期469-482,共14页
Semivarying coefficient models are frequently used in statistical models.In this paper,under the condition that the coefficient functions possess different degrees of smoothness,a two-stepmethod is proposed.In the cas... Semivarying coefficient models are frequently used in statistical models.In this paper,under the condition that the coefficient functions possess different degrees of smoothness,a two-stepmethod is proposed.In the case,one-step method for the smoother coefficient functions cannot beoptimal.This drawback can be repaired by using the two-step estimation procedure.The asymptoticmean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate ofconvergence.A few simulation studies are conducted to evaluate the proposed estimation methods. 展开更多
关键词 Local polynomial regression one-step estimation optimal rate of convergence semi-varying coefficient model two-step estimation.
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Weighted Profile Least Squares Estimation for a Panel Data Varying-Coefficient Partially Linear Model 认领 引用 被引量：1
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作者 Bin ZHOU Jinhong YOU +1 位作者 Qinfeng XU Gemai CHEN 《Chinese Annals of Mathematics,Series B》 SCIE 2010年第2期247-272,共26页
This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model （due to Balt... This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model （due to Baltagi 1995） to the setting of semiparametric regressions. The authors propose a weighted profile least squares estimator （WPLSE） and a weighted local polynomial estimator （WLPE） for the parametric and nonparametric components, respectively. It is shown that the WPLSE is asymptotically more efficient than the usual profile least squares estimator （PLSE）, and that the WLPE is also asymptotically more efficient than the usual local polynomial estimator （LPE）. The latter is an interesting result. According to Ruckstuhl, Welsh and Carroll （2000） and Lin and Carroll （2000）, ignoring the correlation structure entirely and ＂pretending＂ that the data are really independent will result in more efficient estimators when estimating nonparametric regression with longitudinal or panel data. The result in this paper shows that this is not true when the design points of the nonparametric component have a closeness property within groups. The asymptotic properties of the proposed weighted estimators are derived. In addition, a block bootstrap test is proposed for the goodness of fit of models, which can accommodate the correlations within groups illustrate the finite sample performances of the Some simulation studies are conducted to proposed procedures. 展开更多
关键词 Semiparametric Panel data Local polynomial Weighted estimation Block bootstrap
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