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 .
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Zhang, B. Estimating a distribution function in the presence of auxiliary information. Metrika 46, 221–244 (1997). https://doi.org/10.1007/BF02717176
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DOI: https://doi.org/10.1007/BF02717176