Berry–Esseen bound of wavelet estimators in heteroscedastic regression model with random errors

ABSTRACTFor the heteroscedastic regression model Yi=xiβ+g(ti)+σiei, 1≤i≤n, where σi2=f(ui), (xi,ti,ui) are known to be nonrandom design points, g(⋅) and f(⋅) are defined on the closed interval [0,1]. When f(⋅) is known, we investigate the Berry–Esseen type bounds for wavelet estimators of β and g(⋅) under {ei} are identically distributed ϕ-mixing random errors, when f(⋅) is unknown, the Berry–Esseen type bounds for wavelet estimators of β, g(⋅) and f(⋅) established under {ei} are independent random errors.