Estimator In Nonparametric Regression Model Research Articles

Strong laws for weighted sums of widely orthant dependent random variables and applications

Abstract In this study, the strong law of large numbers and the convergence rate for weighted sums of non-identically distributed widely orthant dependent random variables are established. As applications, the strong consistency for weighted estimator in nonparametric regression model and the rate of strong consistency for least-squares estimator in multiple linear regression model are obtained. Some numerical simulations are also provided to verify the validity of the theoretical results.

On estimation of nonparametric regression models with autoregressive and moving average errors

On estimation of nonparametric regression models with autoregressive and moving average errors

Uniformly asymptotic normality of the weighted estimator in nonparametric regression model with φ-mixing errors

Abstract Consider the following nonparametric model: Y ni =g(x ni )+ε ni , 1 ⩽ i ⩽ n, where x n i ∈ A $ x_{ni}\in \mathbb{A} $ are the nonrandom design points and A $ \mathbb{A} $ is a compact set of ℝ m for some m=1, g (·) is a real valued function defined on A $ \mathbb{A} $ , and ε n1, ⋅, ε nn are zero mean φ-mixing random errors with finite moment of 2+δ order for some δ>0. Under some general conditions, we obtain the uniformly asymptotic normality of the weighted estimator of g (·). The rate of Berry-Esseen bound can approximate O(n −1/4) under some appropriate conditions. The validity of the main results is partially illustrated via a numerical simulation.

Complete consistency for the estimator of nonparametric regression model based on m-END errors

Abstract In this paper, we study the complete consistency for the estimator of nonparametric regression model based on m-END errors and obtain the convergence rates of the complete consistency under more general conditions. Finally, some simulations are illustrated to verify the validity of our results.

Consistency properties for the wavelet estimator in nonparametric regression model with dependent errors

In this paper, we establish the pth mean consistency, complete consistency, and the rate of complete consistency for the wavelet estimator in a nonparametric regression model with m-extended negatively dependent random errors. We show that the best rates can be nearly O(n^{-1/3}) under some general conditions. The results obtained in the paper markedly improve and extend some corresponding ones to a much more general setting.

Estimation of nonparametric regression models by wavelets

Estimation of nonparametric regression models by wavelets

On consistency of the weighted estimator in nonparametric regression model with asymptotically almost negatively associated random variables

This paper is concerned with the consistency of nonparametric regression model. For the weighted estimator of unknown regression function, the strong consistency, the complete consistency and the convergence rate of the complete consistency are investigated under some mild conditions. These results extend or improve the corresponding ones of Yang et al. (2018) for extended negatively dependent (END, for short) random variables to asymptotically almost negatively associated random variables. Also, the simulation study of the finite samples provided in this paper shows the validity of our results.

On Complete Consistency for the Estimator of Nonparametric Regression Model Based on Asymptotically Almost Negatively Associated Errors

In this paper, we mainly study the consistency for the estimator of nonparametric regression model based on asymptotically almost negatively associated (AANA, in short) errors. Firstly, the Bernstein type inequality for AANA random variables is established. By using the Bernstein type inequality and moment inequalities, we investigate the complete consistency and convergence rate for the estimator of nonparametric regression model based on AANA errors. As applications, the complete consistency and convergence rate for the nearest neighbor estimator are obtained.

Complete consistency for the estimator of nonparametric regression model based on martingale difference errors

In this paper, we study the complete consistency for the estimator of nonparametric regression model based on martingale difference errors, and obtain the convergence rates of the complete consistency by using the inequalities for martingale difference sequence. Finally, some simulations are illustrated.

Complete convergence for weighted sums of WNOD random variables and its applications

ABSTRACTIn this paper, we mainly studied the complete convergence for weighted sums of widely negative orthant dependent (WNOD, in short) random variables. Some sufficient conditions to prove the complete convergence are provided. As an application, the complete consistency for the weighted estimator of nonparametric regression model is established, and the simulation study is provided to evaluate the finite sample performance of the consistency for the nearest neighbour weight function estimator.

Consistency of the Priestley\u2013Chao estimator in nonparametric regression model with widely orthant dependent errors

In this paper, we establish the strong consistency and complete consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors under some general conditions. We also obtain the rates of strong consistency and complete consistency. We show that the rates can approximate to O(n^{-1/3}) under appropriate conditions. The results obtained in the paper improve or extend the corresponding ones to widely orthant dependent assumptions.

Consistency for wavelet estimator in nonparametric regression model with extended negatively dependent samples

In this article, we mainly study the consistency properties of wavelet estimator in nonparametric regression model with extended negatively dependent samples. Under some suitable conditions, the pth mean consistency, complete consistency and complete consistency rates of the wavelet estimator in nonparametric regression model with extended negatively dependent samples are obtained. Our results generalize or improve the corresponding ones and the wavelet estimator method for independent and mixing dependent samples to some extent.

Limit behaviors of the estimator of nonparametric regression model based on martingale difference errors

In the paper, we shall establish some limit theorems for the nonparametric estimator of the regression model, which include Lp-convergence, complete convergence, and strong convergence of the estimator. These results supplement and improve some known works.

THE CONSISTENCY FOR THE WEIGHTED ESTIMATOR OF NON-PARAMETRIC REGRESSION MODEL BASED ON WIDELY ORTHANT-DEPENDENT ERRORS

In this paper, the complete consistency for the weighted estimator of non-parametric regression model based on widely orthant-dependent errors is established, where the restriction imposed on the dominating coefficient g(n) is very general. Moreover, under some stronger moment condition, we further obtain the convergence rate of the complete consistency, where the assumption on the dominating coefficient g(n) is also very general.

Minimax robust designs for wavelet estimation of nonparametric regression models with autocorrelated errors

We discuss the construction of designs for estimation of nonparametric regression models with autocorrelated errors when the mean response is to be approximated by a finite order linear combination of dilated and translated versions of the Daubechies wavelet bases with four vanishing moments. We assume that the parameters of the resulting model will be estimated by weighted least squares (WLS) or by generalized least squares (GLS). The bias induced by the unused components of the wavelet bases, in the linear approximation, then inflates the natural variation of the WLS and GLS estimates. We therefore construct our designs by minimizing the maximum value of the average mean squared error (AMSE). Such designs are said to be robust in the minimax sense. Our illustrative examples are constructed by using the simulated annealing algorithm to select an optimal [Formula: see text]-point design, which are integers, from a grid of possible values of the explanatory or design variable [Formula: see text]. We found that the integer-valued designs we constructed based on GLS estimation, have smaller minimum loss when compared to the designs for WLS or ordinary least squares (OLS) estimation, except when the correlation parameter [Formula: see text] approaches 1.

Complete convergence for weighted sums of END random variables and its application to nonparametric regression models

ABSTRACTIn this article, the complete convergence for weighted sums of extended negatively dependent (END, for short) random variables is investigated. Some sufficient conditions for the complete convergence are provided. In addition, the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of END random variables is obtained. The results obtained in the article generalise and improve the corresponding one of Wang et al. [(2014b), ‘On Complete Convergence for an Extended Negatively Dependent Sequence’, Communications in Statistics-Theory and Methods, 43, 2923–2937]. As an application, the complete consistency for the estimator of nonparametric regression model is established.

Nonparametric Regression Estimation with Mixed Measurement Errors

We consider the estimation of nonparametric regression models with predictors being measured with a mixture of Berkson and classical errors. In practice, the Berkson error arises when the variable X of interest is unobservable and only a proxy of X can be measured while the inaccuracy related to the observation of the proxy causes an error of classical type. In this paper, we propose two nonparametric estimators of the regression function in the presence of either or both types of errors. We prove the asymptotic normality of our estimators and derive their rates of convergence. The finite-sample properties of the estimators are investigated through simulation studies.

The consistency for the estimator of nonparametric regression model based on martingale difference errors

In this paper, by using the inequalities for martingale difference sequence, we investigate the consistency for the estimator of nonparametric regression model based on martingale difference errors. Some results on consistency for the estimator of \(g(x)\) are presented, including the mean consistency, complete consistency and strong consistency. As an application, the consistency for the nearest neighbor estimator is obtained.

Complete consistency of the estimator of nonparametric regression model under ND sequence

In this paper, we study the complete consistency of estimator of nonparametric regression model based on negatively dependent errors by using the classical Rosenthal-type inequality and the truncated method. As an application, the complete consistency for the nearest neighbor estimator is obtained.

On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models

In this paper, some probability inequalities and moment inequalities for widely orthant-dependent (WOD, in short) random variables are presented, especially the Marcinkiewicz–Zygmund type inequality and Rosenthal type inequality. By using these inequalities, we further study the complete convergence for weighted sums of arrays of row-wise WOD random variables and give some special cases, which extend some corresponding ones for dependent sequences. As applications, we present some sufficient conditions to prove the complete consistency for the estimator of nonparametric regression model based on WOD errors by using the complete convergence that we established. At last, the choice of the fixed design points and the weight functions for the nearest neighbor estimates is proposed. Our results generalize some known results for independent random variables and some dependent random variables.