缺失数据情形概率密度函数的统计推断.pdfVIP

: (1). The conditions in Wang(2008) are weaked (mainly reflect to expand the scope of kernel estimation), we developed semiparametric regression imputation approaches to estimate the prob- ability densitys. Asymptotic normality of the estimators is established, which is used to construct normal approximation based confidence intervals on the the parametric and nonparametric parts. (2). We develop inverse probability weighted approaches to estimate the probability density. Asymptotic normality of the estimators is established, which is used to construct normal approxi- mation based confidence intervals on the probability density In chapter 3 of this paper, under incomplete data and MAR missing mechanism, the construc- tion of Empirical likelihood (EL) confidence intervals for the probability density is studied for the first time. We obtain two results: (1). We use semiparametric regression imputation approach to fill in incomplete data . Based on this imputation approach, EL ratio statistics on the probability density is constructed, which asymptotically has a weighted sum of chi-squared variables. The results is used to obtain EL based confidence intervals on the probability density .in which the adjustment coefficient needs to be estimated. This would lead to a loss of the accuracy of the confidence intervals. (2). We use the inverse probability weighted imputation approach to fill in incomplete data .. Based on this imputation approach, EL ratio statistics on the probability densitys are constructed, which asymptotically have chi-squared distributions. These results are used to obtain EL based confidence intervals on the parametric and nonparametric parts without adjustment, which can improve the accuracy of the confidence intervals. Here we summary some innovations in this paper. 1. The conditions of Wang(Probability density estimation