ASYMPTOTIC NORMALITY OF WAVELET ESTIMATOR IN HETEROSCEDASTIC MODEL WITH α-MIXING ERRORS

Consider heteroscedastic regression model Y=g(x)+σε(1≤i≤n),whereσ~2=f(u),the design points(x,u) are known and nonrandom,g(·) and f(·) are unknown functions defined on closed interval[0,1],and the random errors {ε,1≤i≤n} are assumed to have the same distribution as {ξ,≤i≤n},which is a stationary andα-mixing time series with Eξ=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.