半参数模型误差分布小波估计的渐近理论

Asymptotic Theory of Wavelat Estimation of Error Distribution for a Semiparamatric Model

考虑半参数模型Y＝XTβ＋g（T）＋ε，其误差是i．i．d随机变量，具有公共未知密度f（t）．基于残差构造f（t）的小波估计（t），在适当条件下，证明了该估计的弱相合、强相合、渐近正态性和收敛速度．

For a semiparametric model Y = XTβ + g(t) + ε, let the error seqence be i. i. d with common unknown density f(t) and fmn (t) be a wavelet estimate or of f(t) based on the residuals. Under appropriate condihons, we prove that the estimators convemp in probability and almost everywhere. Asymptotic normality and the rate 0f convergence of the estimator are also considered.