Asymptotic Normality for Wavelet Estimators in Heteroscedastic Semiparametric Model with Random Errors

Abstract

For the heteroscedastic regression model Yi = xiβ + g(ti) + σiei, 1 ≤ i ≤ n, where σ 2 = f (ui), the design points (xi, ti, ui) are known and nonrandom, g(·) and f(·) are defined on the closed interval [0,1]. When f(·) is known, we investigate the asymptotic normality for wavelet estimators of β and g(·) under {ei, 1 ≤ i ≤ n} is a sequence of identically distributed a-mixing errors; when f(·) is unknown, the asymptotic normality for wavelet estimators of β, g(·) and f(·) are established under independent errors. A simulation study is provided to illustrate the feasibility of the theoretical result that the authors derived.