scholarly journals Asymptotic properties of wavelet estimators in semiparametric regression models under dependent errors

2013 ◽  
Vol 122 ◽  
pp. 251-270 ◽  
Author(s):  
Xing-cai Zhou ◽  
Jin-guan Lin
Keyword(s):  
Regression Models ◽  
Asymptotic Properties ◽  
Semiparametric Regression ◽  
Wavelet Estimators

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 Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models

1996 ◽  
Vol 12 (1) ◽  
pp. 30-60 ◽  
Author(s):  
Oliver Linton
Keyword(s):  
Regression Models ◽  
Asymptotic Properties ◽  
Semiparametric Regression ◽  
Higher Order ◽  
Econometric Models ◽  
Discussion Paper ◽  
Stochastic Expansion ◽  
Regression Estimators ◽  
Edgeworth Approximation

We examine the higher order asymptotic properties of semiparametric regression estimators that were obtained by the general MINPIN method described in Andrews (1989, Semiparametric Econometric Models: I. Estimation, Discussion paper 908, Cowles Foundation). We derive an order n−1 stochastic expansion and give a theorem justifying order n−1 distributional approximation of the Edgeworth type.

scholarly journals Robust Statistical Inference in Generalized Linear Models Based on Minimum Renyi’s Pseudodistance Estimators

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 123
Author(s):  
María Jaenada ◽  
Leandro Pardo
Keyword(s):  
Generalized Linear Models ◽  
Influence Function ◽  
Regression Models ◽  
Linear Models ◽  
Asymptotic Properties ◽  
Significant Loss ◽  
Superior Performance ◽  
Test Statistics ◽  
Linear Regression Models ◽  
Type Test

Minimum Renyi’s pseudodistance estimators (MRPEs) enjoy good robustness properties without a significant loss of efficiency in general statistical models, and, in particular, for linear regression models (LRMs). In this line, Castilla et al. considered robust Wald-type test statistics in LRMs based on these MRPEs. In this paper, we extend the theory of MRPEs to Generalized Linear Models (GLMs) using independent and nonidentically distributed observations (INIDO). We derive asymptotic properties of the proposed estimators and analyze their influence function to asses their robustness properties. Additionally, we define robust Wald-type test statistics for testing linear hypothesis and theoretically study their asymptotic distribution, as well as their influence function. The performance of the proposed MRPEs and Wald-type test statistics are empirically examined for the Poisson Regression models through a simulation study, focusing on their robustness properties. We finally test the proposed methods in a real dataset related to the treatment of epilepsy, illustrating the superior performance of the robust MRPEs as well as Wald-type tests.

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