摘要
Consider the heteroscedastic regression model Yi = g（xi） ＋ σiei, 1 ≤ i ≤ n, where σi^2 = f（ui）, here （xi, ui） being fixed design points, g and f being unknown functions defined on [0, 1], ei being independent random errors with mean zero. Assuming that Yi are censored randomly and the censored distribution function is known or unknown, we discuss the rates of strong uniformly convergence for wavelet estimators of g and f, respectively. Also, the asymptotic normality for the wavelet estimators of g is investigated.
Consider the heteroscedastic regression model Yi = g（xi） ＋ σiei, 1 ≤ i ≤ n, where σi^2 = f（ui）, here （xi, ui） being fixed design points, g and f being unknown functions defined on [0, 1], ei being independent random errors with mean zero. Assuming that Yi are censored randomly and the censored distribution function is known or unknown, we discuss the rates of strong uniformly convergence for wavelet estimators of g and f, respectively. Also, the asymptotic normality for the wavelet estimators of g is investigated.
基金
the National Natural Science Foundation of China(10571136)
a Wonkwang University Grant in 2007
