Comparing Edgeworth Expansion and Saddlepoint Approximation in Assessing the Asymptotic Normality Behavior of A Non-Parametric Estimator for Finite Population Total

Abstract

Sample surveys concern themselves with drawing inferences about the population based on sample statistics. We assess the asymptotic normality behavior of a proposed nonparametric estimator for finite a population total based on Edgeworth expansion and Saddlepoint approximation. Three properties; unbiasedness, efficiency and coverage probability of the proposed estimators are compared. Based on the background of the two techniques, we focus on confidence interval and coverage probabilities. Simulations on three theoretical data variables in R, revealed that Saddlepoint approximation performed better than Edgeworth expansion. Saddlepoint approximation resulted into a smaller MSE, tighter confidence interval length and higher coverage probability compared to Edgeworth Expansion. The two techniques should be improved in estimation of parameters in other sampling schemes like cluster sampling.