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BOOTSTRAP WAVELET IN THE NONPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT PROCESSES 认领 引用 被引量：1
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作者 林路 张润楚 《Acta Mathematica Scientia》 SCIE 2004年第1期61-70,共10页
This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of... This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes. 展开更多
关键词 Nonparametric regression weakly dependent process bootstrap wavelet
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Floating Car Data Based Nonparametric Regression Model for Short-Term Travel Speed Prediction 认领 引用 被引量：2
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作者 翁剑成 扈中伟 +1 位作者 于泉 任福田 《Journal of Southwest Jiaotong University(English Edition)》 2007年第3期223-230,共8页
A K-nearest neighbor （K-NN） based nonparametric regression model was proposed to predict travel speed for Beijing expressway. By using the historical traffic data collected from the detectors in Beijing expressways,... A K-nearest neighbor （K-NN） based nonparametric regression model was proposed to predict travel speed for Beijing expressway. By using the historical traffic data collected from the detectors in Beijing expressways, a specically designed database was developed via the processes including data filtering, wavelet analysis and clustering. The relativity based weighted Euclidean distance was used as the distance metric to identify the K groups of nearest data series. Then, a K-NN nonparametric regression model was built to predict the average travel speeds up to 6 min into the future. Several randomly selected travel speed data series, collected from the floating car data （FCD） system, were used to validate the model. The results indicate that using the FCD, the model can predict average travel speeds with an accuracy of above 90%, and hence is feasible and effective. 展开更多
关键词 K-Nearest neighbor Short-term prediction Travel speed Nonparametric regression Intelligence transportation system（ ITS ） Floating car data （FCD）
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Testing heteroscedasticity in nonparametric regression models based on residual analysis 认领 引用 被引量：1
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作者 ZHANG Lei MEI Chang-lin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE 2008年第3期265-272,共8页
The importance of detecting heteroscedasticity in regression analysis is widely recognized because efficient inference for the regression function requires that heteroscedasticity should be taken into account. In this... The importance of detecting heteroscedasticity in regression analysis is widely recognized because efficient inference for the regression function requires that heteroscedasticity should be taken into account. In this paper, a simple test for heteroscedasticity is proposed in nonparametric regression based on residual analysis. Furthermore, some simulations with a comparison with Dette and Munk＇s method are conducted to evaluate the performance of the proposed test. The results demonstrate that the method in this paper performs quite satisfactorily and is much more powerful than Dette and Munk＇s method in some cases. 展开更多
关键词 heteroscedasticity nonparametric regression residual analysis
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Strong Convergence of Partitioning Estimation for Nonparametric Regression Function under Dependence Samples 认领 引用 被引量：7
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作者 LING Neng-xiang DU Xue-qiao 《Chinese Quarterly Journal of Mathematics》 北大核心 2005年第1期28-33,共6页
In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; ... In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; partitioning estimation; strong convergence;φ-mixing sequences. 展开更多
关键词 nonparametric regression function partitioning estimation strong convergence φ-mixing sequences
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Using Evolutionary Computation to Solve Problems in Nonparametric Regression 认领 引用 被引量：2
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作者 Ding Lixin Kang Lishan +1 位作者 Chen Yuping Pan Zhengjun 《Wuhan University Journal of Natural Sciences》 EI CAS 1998年第1期27-31,共5页
This paper studies evolutionary mechanism of parameter selection in the construction of weight function for Nearest Neighbour Estimate in nonparametric regression. Construct an algorithm which adaptively evolves fine ... This paper studies evolutionary mechanism of parameter selection in the construction of weight function for Nearest Neighbour Estimate in nonparametric regression. Construct an algorithm which adaptively evolves fine weight and makes good prediction about unknown points. The numerical experiments indicate that this method is effective. It is a meaningful discussion about practicability of nonparametric regression and methodology of adaptive model-building. 展开更多
关键词 nonparametric regression Nearest Neighbour Estimate evolutionary computation nonhomogeneous selection adaptive model-building
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Asymptotic Property for the Estimator of Nonparametric Regression Models Under Negatively Orthant Dependent Errors 认领 引用 被引量：1
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作者 PENG Zhi-qing ZHENG Lu-lu LIU Yah-fang XIAO Ru WANG Xue-jun 《Chinese Quarterly Journal of Mathematics》 2015年第2期300-307,共8页
In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete co... In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented. 展开更多
关键词 negatively orthant dependent random variables nonparametric regression model complete consistency
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ASYMPTOTICS OF THE RESIDUALS DENSITY ESTIMATION IN NONPARAMETRIC REGRESSION UNDER m(n)-DEPENDENT SAMPLE 认领 引用
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作者 QIN GENGSHENG SHI SUNJUAN CHAI GENXIANG Department of Mathematics, Sichuan University Chengdu 610064 Department of Mathematics, Sichuan Educational College, Chengdu 610061 Department of Applied Mathematics, Tongji University Shanghai 200092. 《Applied Mathematics(A Journal of Chinese Universities)》 1996年第1期59-76,共18页
Let Y_i=M(X_i)+ei, where M(x)=E(Y|X=x) is an unknown realfunction on B(? R), {(X_1,Y_i)} is a stationary and m(n)-dependent sample from(X, Y), the residuals {e_i} are independent of {X_i} and have unknown common densi... Let Y_i=M(X_i)+ei, where M(x)=E(Y|X=x) is an unknown realfunction on B(? R), {(X_1,Y_i)} is a stationary and m(n)-dependent sample from(X, Y), the residuals {e_i} are independent of {X_i} and have unknown common densityf(x). In [2] a nonparametric estimate f_n(x) for f(x) has been proposed on the basisof the residuals estimates. In this paper, we further obtain the asymptotic normalityand the law of the iterated logarithm of f_n(x) under some suitable conditions. Theseresults together with those in [2] bring the asymptotic theory for the residuals densityestimate in nonparametric regression under m(n)-dependent sample to completion. 展开更多
关键词 Nonparametric regression residuals asymptotic normality iterated logarithm m(n)-dependent sample
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Longitudinal Survey, Nonmonotone, Nonresponse, Imputation, Nonparametric Regression 认领 引用
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作者 Sarah Pyeye Charles K. Syengo +2 位作者 Leo Odongo George O. Orwa Romanus O. Odhiambo 《Open Journal of Statistics》 2016年第6期1138-1154,共17页
The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-depend... The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-dependent finite populations means. The asymptotic properties (unbiasedness and consistency) of the proposed estimator are investigated. Comparisons between different parametric and nonparametric estimators are performed based on the bootstrap standard deviation, mean square error and percentage relative bias. A simulation study is carried out to determine the best performing estimator of the time-dependent finite population means. The simulation results show that local linear regression estimator yields good properties. 展开更多
关键词 Longitudinal Survey Nonmonotone Nonresponse Imputation Nonparametric Regression
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Nonparametric Regression Algorithm for Short-term Traffic Flow Forecasting Based on Data Reduction and Support Vector Machine 认领 引用
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作者 WU Jin-wu ZHANG Hai-feng RAN Xu-dong 《Journal of Highway and Transportation Research and Development(English Edition)》 2020年第3期96-103,共8页
Nonparametric regression is an important method for short-term traffic flow forecasting,but the traditional nonparametric regression method needs a large storage space and slow query speed when the data are large and ... Nonparametric regression is an important method for short-term traffic flow forecasting,but the traditional nonparametric regression method needs a large storage space and slow query speed when the data are large and the dimension is high.In this paper,an improved nonparametric regression traffic flow forecasting algorithm is proposed.Subtraction fuzzy clustering method is used to cluster historical data to reduce the amount of data in the pattern database.Principal component analysis(PCA)is used to reduce the dimension of the pattern to overcome the problems of slow matching speed and interference of irrelevant dimension caused by the high dimension of the pattern.The support vector machine method is used to estimate the value of the final predicted variables by searching the patterns.The operation efficiency and prediction accuracy of the algorithm are improved.An online simulation-based test shows that the algorithm exhibits better efficiency and accuracy compared with traditional methods. 展开更多
关键词 ITS short-term traffic flow forecasting nonparametric regression algorithm data reduction intelligent transport
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CONFIDENCE INTERVALS FOR NONPARAMETRIC REGRESSION FUNCTIONS WITH MISSING DATA:MULTIPLE DESIGN CASE 认领 引用 被引量：2
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作者 Qingzhu LEI Yongsong QIN 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2011年第6期1204-1217,共14页
This paper considers two estimators ofθ=g(x)in a nonparametric regression model Y=g(x)+ε(x∈(0,1)p)with missing responses:Imputation and inverse probability weighted esti-mators.Asymptotic normality of the two estim... This paper considers two estimators ofθ=g(x)in a nonparametric regression model Y=g(x)+ε(x∈(0,1)p)with missing responses:Imputation and inverse probability weighted esti-mators.Asymptotic normality of the two estimators is established,which is used to construct normal approximation based confidence intervals onθ. 展开更多
关键词 Confidence interval missing at random nonparametric regression normal approximation.
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Robust Depth-Weighted Wavelet for Nonparametric Regression Models 认领 引用 被引量：6
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作者 Lu LIN 《Acta Mathematica Sinica,English Series》 SCIE 2005年第3期585-592,共8页
In the nonparametric regression models, the original regression estimators including kernel estimator, Fourier series estimator and wavelet estimator are always constructed by the weighted sum of data, and the weights... In the nonparametric regression models, the original regression estimators including kernel estimator, Fourier series estimator and wavelet estimator are always constructed by the weighted sum of data, and the weights depend only on the distance between the design points and estimation points. As a result these estimators are not robust to the perturbations in data. In order to avoid this problem, a new nonparametric regression model, called the depth-weighted regression model, is introduced and then the depth-weighted wavelet estimation is defined. The new estimation is robust to the perturbations in data, which attains very high breakdown value close to 1/2. On the other hand, some asymptotic behaviours such as asymptotic normality are obtained. Some simulations illustrate that the proposed wavelet estimator is more robust than the original wavelet estimator and, as a price to pay for the robustness, the new method is slightly less efficient than the original method. 展开更多
关键词 Nonparametric regression Wavelet Statistical depth Robustness
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Wavelet Detection and Estimation of Change Points in Nonparametric Regression Models under Random Design 认领 引用 被引量：2
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作者 ZHAO Wen Zhi TIAN Zheng XIA Zhi Ming 《Journal of Mathematical Research and Exposition》 2009年第2期247-256,共10页
A wavelet method of detection and estimation of change points in nonparametric regression models under random design is proposed. The confidence bound of our test is derived by using the test statistics based on empir... A wavelet method of detection and estimation of change points in nonparametric regression models under random design is proposed. The confidence bound of our test is derived by using the test statistics based on empirical wavelet coefficients as obtained by wavelet transformation of the data which is observed with noise. Moreover, the consistence of the test is proved while the rate of convergence is given. The method turns out to be effective after being tested on simulated examples and applied to IBM stock market data. 展开更多
关键词 random design nonparametric regression model change point wavelet transformation consistent test rate of convergence.
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Fixed Design Nonparametric Regression with Truncated and Censored Data 认领 引用 被引量：1
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作者 Liu-quan SunAcademy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China 《Acta Mathematicae Applicatae Sinica》 2003年第2期229-238,共10页
Abstract In this paper we consider a fixed design model in which the observations are subject to left truncation and right censoring. A generalized product-limit estimator for the conditional distribution at a given c... Abstract In this paper we consider a fixed design model in which the observations are subject to left truncation and right censoring. A generalized product-limit estimator for the conditional distribution at a given covariate value is proposed, and an almost sure asymptotic representation of this estimator is established. We also obtain the rate of uniform consistency, weak convergence and a modulus of continuity for this estimator. Applications include trimmed mean and quantile function estimators.These applications demonstrate the usefulness of the new matrix products. 展开更多
关键词 Keywords Nonparametric regression fixed design asymptotic representation truncated and censored data modulus of continuity
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OPTIMAL GLOBAL RATES OF CONVERGENCE OF M-ESTIMATES FOR MULTIVARIATE NONPARAMETRIC REGRESSION 认领 引用
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作者 施沛德 王学仁 《Acta Mathematicae Applicatae Sinica》 1995年第2期139-151,共13页
Consider the nonparametric regression model Y=go(T)+u, where Y is real-valued, u is a random error, T is a random d-vector of explanatory variables ranging over a nondegenerate d-dimensional compact set C, and go(... Consider the nonparametric regression model Y=go(T)+u, where Y is real-valued, u is a random error, T is a random d-vector of explanatory variables ranging over a nondegenerate d-dimensional compact set C, and go(·) is the unknown smooth regression function, which is m (0) times continuously differentiable and its mth partial derivatives satisfy the Hǒlder condition with exponent γ∈(0,1], where i1, . . . , id are nonnegative integers satisfying ik=m. The piecewise polynomial estimator of go based on M-estimates is considered. It is proved that the rate of convergence of the underlying estimator is Op () under certain regular conditions, which is the optimal global rate of convergence of least square estimates for nonparametric regression studied in [10-11] . 展开更多
关键词 Nonparametric regression global rate of convergence piecewise polynomial Mestimates
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Complete moment convergence for weighted sums of widely orthant-dependent random variables and its application in nonparametric regression models 认领 引用 被引量：1
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作者 Lu CHENG Junjun LANG +1 位作者 Yan SHEN Xuejun WANG 《Frontiers of Mathematics in China》 SCIE CSCD 2022年第4期571-590,共20页
We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent(WOD)random variables,which improve and extend the corresponding results of Y.F.Wu,M.G.Zhai,and J.Y.Peng[J.Math... We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent(WOD)random variables,which improve and extend the corresponding results of Y.F.Wu,M.G.Zhai,and J.Y.Peng[J.Math.Inequal.,2019,13(1):251–260].As an application of the main results,we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results. 展开更多
关键词 Widely orthant-dependent random variables complete moment convergence nonparametric regression model
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Nonparametric Feature Screening via the Variance of the Regression Function 认领 引用
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作者 Won Chul Song Michael G. Akritas 《Open Journal of Statistics》 2024年第4期413-438,共26页
This article develops a procedure for screening variables, in ultra high-di- mensional settings, based on their predictive significance. This is achieved by ranking the variables according to the variance of their res... This article develops a procedure for screening variables, in ultra high-di- mensional settings, based on their predictive significance. This is achieved by ranking the variables according to the variance of their respective marginal regression functions (RV-SIS). We show that, under some mild technical conditions, the RV-SIS possesses a sure screening property, which is defined by Fan and Lv (2008). Numerical comparisons suggest that RV-SIS has competitive performance compared to other screening procedures, and outperforms them in many different model settings. 展开更多
关键词 Sure Independence Screening Nonparametric Regression Ultrahigh-Dimensional Data Variable Selection
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Asymptotics of the“Minimum L_1-Norm”Estimates in Nonparametric Regression Models 认领 引用
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作者 Shi Pei-De Cheng Ping Institute of Systems Science Academia Sinica Beijing,100080 China 《Acta Mathematica Sinica,English Series》 SCIE 1994年第3期276-288,共13页
Consider the nonparametric regression model Y=go（T）+u,where Y is real-valued, u is a random error,T ranges over a nondegenerate compact interval,say[0,1],and go（·）is an unknown regression function,which is m... Consider the nonparametric regression model Y=go（T）+u,where Y is real-valued, u is a random error,T ranges over a nondegenerate compact interval,say[0,1],and go（·）is an unknown regression function,which is m（m≥0）times continuously differentiable and its ruth derivative,g0（m）,satisfies a H■lder condition of order γ（m +γ】1/2）.A piecewise polynomial L1- norm estimator of go is proposed.Under some regularity conditions including that the random errors are independent but not necessarily have a common distribution,it is proved that the rates of convergence of the piecewise polynomial L1-norm estimator are o(n-2（m+γ）+1/m+γ-1/δalmost surely and o(n-2（m+γ）+1/m+γ-δ)in probability,which can arbitrarily approach the optimal rates of convergence for nonparametric regression,where δ is any number in （0, min（（m+γ-1/2）/3,γ））. 展开更多
关键词 Estimates in Nonparametric Regression Models Minimum L1-Norm
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ON THE CONSISTENCY OF CROSS-VALIDATIONIN NONLINEAR WAVELET REGRESSION ESTIMATION 认领 引用
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作者 张双林 郑忠国 《Acta Mathematica Scientia》 SCIE 2000年第1期1-11,共11页
For the nonparametric regression model Y-ni = g(x(ni)) + epsilon(ni)i = 1, ..., n, with regularly spaced nonrandom design, the authors study the behavior of the nonlinear wavelet estimator of g(x). When the threshold ... For the nonparametric regression model Y-ni = g(x(ni)) + epsilon(ni)i = 1, ..., n, with regularly spaced nonrandom design, the authors study the behavior of the nonlinear wavelet estimator of g(x). When the threshold and truncation parameters are chosen by cross-validation on the everage squared error, strong consistency for the case of dyadic sample size and moment consistency for arbitrary sample size are established under some regular conditions. 展开更多
关键词 consistency cross-validation nonparametric regression threshold truncation wavelet estimator
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The M-estimate of Local Linear Regression with Variable Window Breadth 认领 引用
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作者 王新民 董小刚 蒋学军 《Northeastern Mathematical Journal》 2005年第2期153-157,共5页
In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.
关键词 local linear regression M-estimate nonparametric regression
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WAVELET-BASED ESTIMATORS OF MEAN REGRESSION FUNCTION WITH LONG MEMORY DATA 认领 引用
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作者 李林元 肖益民 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第7期901-910,共10页
This paper provides an asymptotic expansion for the mean integrated squared error （MISE） of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying... This paper provides an asymptotic expansion for the mean integrated squared error （MISE） of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel estimators.However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent. 展开更多
关键词 nonlinear wavelet-based estimator nonparametric regression long-range dependence
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