Consistency and uniformly asymptotic normality of wavelet estimator in regression model with associated samples

Consider the wavelet estimator of a nonparametric fixed design regression function when errors are strictly stationary and associated random variables. We establish pointwise weak consistency and uniformly asymptotic normality of wavelet estimator of regression function. We give rates of uniformly a...

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Bibliographic Details
Published in:Statistics & probability letters 2008-12, Vol.78 (17), p.2947-2956
Main Authors: Li, Yongming, Yang, Shanchao, Zhou, Yong
Format: Article
Language:English
Subjects:
Exact sciences and technology
General topics
Mathematics
Nonparametric inference
Parametric inference
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
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Summary:Consider the wavelet estimator of a nonparametric fixed design regression function when errors are strictly stationary and associated random variables. We establish pointwise weak consistency and uniformly asymptotic normality of wavelet estimator of regression function. We give rates of uniformly asymptotic normality for associated samples. The rates are near n − 1 / 4 and n − 1 / 6 when their third moments are finite for NA and PA cases, respectively.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2008.05.004