Bootstrap Variance Estimation for Semiparametric Finite Population Distribution Function Estimator

Abstract

Estimating finite population distribution function (FPDF) emerges as an important problem to the survey statisticians since the pioneering work of Chambers and Dunstan ^[1] . It unifies estimation of standard finite population parameters, namely, mean and quantiles. Regarding this, estimating variance of FPDF estimator is an important task for accessing the quality of the estimtor and drawing inferences (e.g., confidence interval estimation) on finite population parameters. Due to non-linearity of FPDF estimator, resampling-based methods are developed earlier for parametric or non-parametric Chambers–Dunstan estimator. Here, we attempt the problem of estimating variance of P-splines-based semiparametric model-based Chambers–Dunstan type estimator of the FPDF. The proposed variance estimator involes bootstrapping. Here, the bootstrap procedure is non-trivial since it does not imitate the full mechanism of two-stage sample generating procedure from an infinite hypothetical population (superpopulation). We have established the weak consistency of the proposed resampling-based variance estimator for specific sampling designs, e.g., simple random sampling. Also, the satisfactory empirical performance of the poposed estimator has been shown through simulation studies and a real life example.