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

Xing-cai Zhou and Jin-guan Lin

Journal of Multivariate Analysis, 2013, vol. 122, issue C, 251-270

Abstract: Consider the semiparametric regression model yi=xiTβ+g(ti)+εi for i=1,…,n, where xi∈Rp are the random design vectors, ti are the constant sequences on [0,1], β∈Rp is an unknown vector of the slop parameter, g is an unknown real-valued function defined on the closed interval [0,1], and the error random variables εi are coming from a stationary stochastic process, satisfying the strong mixing condition in some results. Under suitable conditions, we obtain expansions for the bias and the variance of wavelet estimators βˆn and gˆn(⋅) of β and g(⋅) respectively, prove their weak consistency, and establish the asymptotic normality and the Berry–Esseen bound of βˆn.

Keywords: Semiparametric regression model; Wavelet estimator; Strong mixing; Weak consistency; Asymptotic normality; Berry–Esseen bound (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (8)

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DOI: 10.1016/j.jmva.2013.08.006

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