Convergence rates of wavelet estimators in semiparametric regression models under NA samples

Consider the following heteroscedastic semiparametric regression model: y(i) = X-i(T)beta + sigma(i)e(i), 1 <= i <= n, where {X-i, 1 <= i <= n} are random design points, errors {e (i), 1 <= i <= n} are negatively associated (NA) random variables, sigma(2)(i) = h(u (i)), and {u(i)} and {t(i)} are two nonrandom sequences on [0, 1]. Some wavelet estimators of the parametric component beta, the nonparametric component g (t) and the variance function h(u) are given. Under some general conditions, the strong convergence rate of these wavelet estimators is . Hence our results are extensions of those results on independent random error settings.