Asymptotic normality of variance estimator in a heteroscedastic model with dependent errors

Han-Ying Liang and Ya-Mei Liu

Journal of Nonparametric Statistics, 2011, vol. 23, issue 2, 351-365

Abstract: Consider the heteroscedastic regression model Yni=g(xni)+σniεni (1≤i≤n), where , the design points (xni, uni) are known and nonrandom, g(·) and f(·) are unknown functions defined on [0, 1], and the random errors {εni, 1≤i≤n} are assumed to have the same distribution as {ξi, 1≤i≤n}, which is a stationary and α-mixing time series with Eξi=0. Under appropriate conditions, we study the asymptotic normality of an estimator of the function f(·). At the same time, we derive a Berry–Esseen-type bound for the estimator. As a corollary, by making a certain choice of the weights, the Berry–Esseen-type bound of the estimator can attain O(n−1/12(log n)−1/3). Finite sample behaviour of this estimator is investigated too.

Date: 2011
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DOI: 10.1080/10485252.2011.552721

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