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

Consider the heteroscedastic regression model Yni=g(xni)+sigma ni epsilon ni (1in), where [image omitted], the design points (xni, uni) are known and nonrandom, g(center dot) and f(center dot) are unknown functions defined on [0, 1], and the random errors {epsilon ni, 1in} are assumed to have the same distribution as {i, 1in}, which is a stationary and -mixing time series with Ei=0. Under appropriate conditions, we study the asymptotic normality of an estimator of the function f(center dot). 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.