Convergence of the local linear estimator for a generalized regression function with heterogeneous dependent functional data

2021 ◽  
Author(s):  
Danilo Matsuoka ◽  
Hudson Torrent
Keyword(s):  
Functional Data ◽  
Regression Function ◽  
Linear Estimator ◽  
Local Linear ◽  
Local Linear Estimator ◽  
Generalized Regression

scholarly journals LOCAL LINEAR FITTING UNDER NEAR EPOCH DEPENDENCE: UNIFORM CONSISTENCY WITH CONVERGENCE RATES

2012 ◽  
Vol 28 (5) ◽  
pp. 935-958 ◽  
Author(s):  
Degui Li ◽  
Zudi Lu ◽  
Oliver Linton
Keyword(s):  
Convergence Rates ◽  
Regression Function ◽  
Linear Estimator ◽  
Uniform Consistency ◽  
Linear Fitting ◽  
Semiparametric Modeling ◽  
Local Linear Fitting ◽  
Local Linear ◽  
Local Linear Estimator ◽  
Nonparametric Kernel

Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton (2007, Econometric Theory23, 37–70) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results regarding uniform convergence rates for nonparametric kernel-based estimators are provided. The results of this paper will be of wide potential interest in time series semiparametric modeling.

scholarly journals Bayesian bandwidth estimation for local linear fitting in nonparametric regression models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Han Lin Shang ◽  
Xibin Zhang
Keyword(s):  
Regression Model ◽  
Nonparametric Regression ◽  
Regression Function ◽  
Linear Estimator ◽  
Bandwidth Estimation ◽  
Nonparametric Regression Model ◽  
Mixture Density ◽  
Local Linear ◽  
Local Linear Estimator ◽  
Error Density

AbstractThis paper presents a Bayesian sampling approach to bandwidth estimation for the local linear estimator of the regression function in a nonparametric regression model. In the Bayesian sampling approach, the error density is approximated by a location-mixture density of Gaussian densities with means the individual errors and variance a constant parameter. This mixture density has the form of a kernel density estimator of errors and is referred to as the kernel-form error density (c.f. Zhang, X., M. L. King, and H. L. Shang. 2014. “A Sampling Algorithm for Bandwidth Estimation in a Nonparametric Regression Model with a Flexible Error Density.” Computational Statistics & Data Analysis 78: 218–34.). While (Zhang, X., M. L. King, and H. L. Shang. 2014. “A Sampling Algorithm for Bandwidth Estimation in a Nonparametric Regression Model with a Flexible Error Density.” Computational Statistics & Data Analysis 78: 218–34) use the local constant (also known as the Nadaraya-Watson) estimator to estimate the regression function, we extend this to the local linear estimator, which produces more accurate estimation. The proposed investigation is motivated by the lack of data-driven methods for simultaneously choosing bandwidths in the local linear estimator of the regression function and kernel-form error density. Treating bandwidths as parameters, we derive an approximate (pseudo) likelihood and a posterior. A simulation study shows that the proposed bandwidth estimation outperforms the rule-of-thumb and cross-validation methods under the criterion of integrated squared errors. The proposed bandwidth estimation method is validated through a nonparametric regression model involving firm ownership concentration, and a model involving state-price density estimation.

A Recursive Local Linear Estimator for Identification of Nonlinear ARX Systems: Asymptotical Convergence and Applications

2013 ◽  
Vol 58 (12) ◽  
pp. 3054-3069 ◽  
Author(s):  
Wenxiao Zhao ◽  
Wei Xing Zheng ◽  
Er-Wei Bai
Keyword(s):  
Linear Estimator ◽  
Local Linear ◽  
Local Linear Estimator ◽  
Asymptotical Convergence

scholarly journals Modeling of diabetes mellitus risk based on consumption of salt, sugar, and fat factors using local linear estimator

2020 ◽  
Author(s):  
W. A. Anam ◽  
A. Massaid ◽  
N. A. Amesya ◽  
N. Chamidah
Keyword(s):  
Diabetes Mellitus ◽  
Linear Estimator ◽  
Local Linear ◽  
Local Linear Estimator ◽  
Diabetes Mellitus Risk

scholarly journals Rate of the Almost Sure Convergence of a Generalized Regression Estimate Based on Truncated and Functional Data

2020 ◽  
pp. 480-491
Author(s):  
Halima Boudada ◽  
Sara Leulmi ◽  
Soumia Kharfouch
Keyword(s):  
Functional Data ◽  
Dimensional Space ◽  
Almost Sure Convergence ◽  
Regression Function ◽  
Random Variable ◽  
Infinite Dimensional Space ◽  
Left Truncation ◽  
Regression Estimate ◽  
Infinite Dimensional ◽  
Generalized Regression

In this paper, a nonparametric estimation of a generalized regression function is proposed. The real response random variable (r.v.) is subject to left-truncation by another r.v. while the covariate takes its values in an infinite dimensional space. Under standard assumptions, the pointwise and the uniform almost sure convergences, of the proposed estimator, are established

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