Estimating a distribution function in the presence of auxiliary information

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