Convergence Rates of Wavelet Estimators in Semiparametric Regression Models Under NA Samples

Consider the following heteroscedastic semiparametric regression model: y_i = Xi T β + g（ti） + σiei, 1 ≤ i ≤ n, where {Xi, 1 ≤ i ≤ n} are random design points, errors {ei, 1 ≤ i ≤ n} are negatively associated （NA） random variables, σi2 = h（ui）, and {ui} and {ti} are two nonrandom sequences on 0, 1]. Some wavelet estimators of the parametric component β, the non- parametric component g（t） and the variance function h（u） are given. Under some general conditions, the strong convergence rate of these wavelet estimators is O(n^-1/3 log n). Hence our results are extensions of those results on independent random error settings.