Estimation of Finite Population Quantile by Analytical and Re-scaling Bootstrap Techniques

Abstract

Using a large sample drawn from the population by employing a general sampling design, Chaudhuri and Shaw (2020) used a model-assisted design-based approach in deriving asymptotically design-unbiased estimators of finite population distribution function, the associated quantiles and their mean square errors. Anticipating improvement in the accuracy of estimates of population distribution function and quantiles, this paper uses two alternative techniques in revising estimator of the distribution function; a non-linear function of five population totals. This paper presents a linear approximation of this estimator by using Taylor series expansion neglecting the higher order terms and uses this in deriving its approximate mean square error and the mean square error estimate. Alternatively, Rao and Wu (1988) re-scaling bootstrap technique is also used to modify the estimator of the population distribution function. Estimation of population distribution function using the above two alternative techniques, the population quantiles, their standard errors and related confidence intervals are derived. Numerical findings based on real data show gain in efficiency of estimates of both distribution function and quantiles using the two alternative techniques.