Asymptotic normality of wavelet estimator in heteroscedastic model with α-mixing errors

Consider heteroscedastic regression model Yni = g(xni) + σniɛni (1 ≤ i ≤ n), where σni2 = f(uni), the design points (xni, uni) are known and nonrandom, g(·) and f(·) are unknown functions defined on closed interval [0, 1], and the random errors {ɛni, 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 asymptotic normality of wavelet estimators of g(·) and f(·). Finite sample behavior of the estimators is investigated via simulations, too.