scholarly journals Strong consistency rate of estimators in heteroscedastic errors-in-variables model for negative association samples

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4639-4654
Author(s):  
Jing-Jing Zhang ◽  
Ting Wang
Keyword(s):  
Strong Consistency ◽  
Error Variance ◽  
Negative Association ◽  
Variance Function ◽  
Slope Parameter ◽  
Errors In Variables ◽  
Random Errors ◽  
Partially Linear ◽  
Heteroscedastic Errors ◽  
Consistency Rate

This article is concerned with the estimating problem of heteroscedastic partially linear errorsin- variables (EV) models. We derive the strong consistency rate for estimators of the slope parameter and the nonparametric component in the case of known error variance with negative association (NA) random errors. Meanwhile, when the error variance is unknown, the strong consistency rate for the estimators of the slope parameter and the nonparametric component as well as variance function are considered for NA samples. In general, we concluded that the strong consistency rate for all estimators can achieve o(n-1/4).

scholarly journals Statistical Inference for the Heteroscedastic Partially Linear Varying-Coefficient Errors-in-Variables Model with Missing Censoring Indicators

2021 ◽  
Vol 2021 ◽  
pp. 1-26
Author(s):  
Yuye Zou ◽  
Chengxin Wu
Keyword(s):  
Empirical Likelihood ◽  
Error Variance ◽  
Variance Function ◽  
Likelihood Method ◽  
Coefficient Function ◽  
Errors In Variables ◽  
Finite Sample ◽  
Right Censored Data ◽  
Varying Coefficient ◽  
Partially Linear

In this paper, we focus on heteroscedastic partially linear varying-coefficient errors-in-variables models under right-censored data with censoring indicators missing at random. Based on regression calibration, imputation, and inverse probability weighted methods, we define a class of modified profile least square estimators of the parameter and local linear estimators of the coefficient function, which are applied to constructing estimators of the error variance function. In order to improve the estimation accuracy and take into account the heteroscedastic error, reweighted estimators of the parameter and coefficient function are developed. At the same time, we apply the empirical likelihood method to construct confidence regions and maximum empirical likelihood estimators of the parameter. Under appropriate assumptions, the asymptotic normality of the proposed estimators is studied. The strong uniform convergence rate for the estimators of the error variance function is considered. Also, the asymptotic chi-squared distribution of the empirical log-likelihood ratio statistics is proved. A simulation study is conducted to evaluate the finite sample performance of the proposed estimators. Meanwhile, one real data example is provided to illustrate our methods.

scholarly journals Strong Consistency of Estimators in a Partially Linear Model with Asymptotically Almost Negatively Associated Errors

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Yu Zhang ◽  
Xinsheng Liu ◽  
Mohamed Sief
Keyword(s):  
Least Squares ◽  
Strong Consistency ◽  
Weighted Least Squares ◽  
Partially Linear Model ◽  
Random Errors ◽  
Negatively Associated ◽  
Partially Linear ◽  
Least Squares Estimators ◽  
Special Cases ◽  
Asymptotically Almost Negatively Associated

This paper studies a heteroscedastic partially linear regression model in which the errors are asymptotically almost negatively associated (AANA, in short) random variables with not necessarily identical distribution and zero mean. Under some mild conditions, we establish the strong consistency of least squares estimators, weighted least squares estimators, and the ultimate weighted least squares estimators for the unknown parameter, respectively. In addition, the strong consistency of the estimator for nonparametric component is also investigated. The results derived in the paper include the corresponding ones of independent random errors and some dependent random errors as special cases. At last, two simulations are carried out to study the numerical performance of the strong consistency for least squares estimators and weighted least squares estimators of the unknown parametric and nonparametric components in the model.

scholarly journals Asymptotic properties of wavelet estimators in heteroscedastic semiparametric model based on negatively associated innovations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xueping Hu ◽  
Jinbiao Zhong ◽  
Jiashun Ren ◽  
Bing Shi ◽  
Keming Yu
Keyword(s):  
Strong Consistency ◽  
Closed Interval ◽  
Asymptotic Properties ◽  
Semiparametric Regression ◽  
Slope Parameter ◽  
Random Errors ◽  
Semiparametric Regression Model ◽  
Negatively Associated ◽  
Na Random Variables ◽  
Wavelet Estimators

AbstractConsider the heteroscedastic semiparametric regression model $y_{i}=x_{i}\beta+g(t_{i})+\varepsilon_{i}$yi=xiβ+g(ti)+εi, $i=1, 2, \ldots, n$i=1,2,…,n, where β is an unknown slope parameter, $\varepsilon_{i}=\sigma_{i}e_{i}$εi=σiei, $\sigma^{2}_{i}=f(u_{i})$σi2=f(ui), $(x_{i},t_{i},u_{i})$(xi,ti,ui) are nonrandom design points, $y_{i}$yi are the response variables, f and g are unknown functions defined on the closed interval $[0,1]$[0,1], random errors $\{e_{i} \}${ei} are negatively associated (NA) random variables with zero means. Whereas kernel estimators of β, g, and f have attracted a lot of attention in the literature, in this paper, we investigate their wavelet estimators and derive the strong consistency of these estimators under NA error assumption. At the same time, we also obtain the Berry–Esséen type bounds of the wavelet estimators of β and g.

scholarly journals Strong consistency rates of estimators in semi-parametric errors-in-variables model with missing responses

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 6073-6089
Author(s):  
Jingjing Zhang ◽  
Linran Zhang
Keyword(s):  
Measurement Errors ◽  
Strong Consistency ◽  
Missing At Random ◽  
Slope Parameter ◽  
Errors In Variables ◽  
Missing Responses ◽  
Error In Variables ◽  
Response Variables

In this article, we focus on the semi-parametric error-in-variables model with missing responses: yi = ?i? + g(ti)+ ?i,xi = ?i + ?i, where yi are the response variables missing at random, (?i,ti) are design points, ?i are the potential variables observed with measurement errors ?i, the unknown slope parameter ? and nonparametric component g(?) need to be estimate. Here we choose three different approaches to estimate ? and g(?). Under appropriate conditions, we study the strong consistency rates for the proposed estimators. In general, we concluded that the strong consistency rates for all estimators can achieve o(n-1/4).

scholarly journals The Consistency of Estimators in a Heteroscedastic Partially Linear Model with ρ−-Mixing Errors

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1188
Author(s):  
Yu Zhang ◽  
Xinsheng Liu
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Unknown Parameter ◽  
Strong Consistency ◽  
Weighted Least Squares ◽  
Partially Linear Model ◽  
Random Errors ◽  
Partially Linear ◽  
Special Cases ◽  
Theoretical Results

This paper studies a heteroscedastic partially linear model based on ρ − -mixing random errors, stochastically dominated and with zero mean. Under some suitable conditions, the strong consistency and p -th ( p > 0 ) mean consistency of least squares (LS) estimators and weighted least squares (WLS) estimators for the unknown parameter are investigated, and the strong consistency and p -th ( p > 0 ) mean consistency of the estimators for the non-parametric component are also studied. These results include the corresponding ones of independent, negatively associated (NA), and ρ * -mixing random errors as special cases. At last, two simulations are presented to support the theoretical results.

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