Estimating a distribution function in the presence of auxiliary information

Abstract

For estimating the distribution functionF of a population, the empirical or sample distribution functionF _n has been studied extensively. Qin and Lawless (1994) have proposed an alternative estimator$\hat F_n$ for estimatingF in the presence of auxiliary information under a semiparametric model. They have also proved the point-wise asymptotic normality of$\hat F_n$. In this paper, we establish the weak convergence of$\hat F_n$ to a Gaussian process and show that the asymptotic variance function of$\hat F_n$ is uniformly smaller than that ofF _n . As an application of$\hat F_n$, we propose to employ the mean and varianceŜ ² _n of$\hat F_n$ to estimate the population mean and variance in the presence of auxiliary information. A simulation study is presented to assess the finite sample performance of the proposed estimators$\hat F_n$, andŜ ² _n .