Asymptotic properties of wavelet estimators in semiparametric regression models under dependent errors

Consider the semiparametric regression model y i = x i T β + g ( t i ) + ε i for i = 1 , … , n , where x i ∈ R p are the random design vectors, t i are the constant sequences on [ 0 , 1 ] , β ∈ R p is an unknown vector of the slop parameter, g is an unknown real-valued function defined on the closed interval [ 0 , 1 ] , and the error random variables ε i are coming from a stationary stochastic process, satisfying the strong mixing condition in some results. Under suitable conditions, we obtain expansions for the bias and the variance of wavelet estimators β ˆ n and g ˆ n ( ⋅ ) of β and g ( ⋅ ) respectively, prove their weak consistency, and establish the asymptotic normality and the Berry–Esseen bound of β ˆ n .