Coverage probability of a non-parametric estimator for a finite population total using edgeworth expansion
Date
2019
Authors
Okungu, Jacob
Orwa, George
Odhiambo, Romanus
Journal Title
Journal ISSN
Volume Title
Publisher
Strathmore University
Abstract
In survey sampling, the main objective is more often than not to establish information
about any population parameter using the sample statistics. A nonparametric estimator of
the finite population total is proposed. The nonparametric estimator of finite population
total by Dorfman (1992) is developed and the coverage probabilities explored using the
Edgeworth. The asymptotic properties; unbiasedness, efficiency and coverage rates of the
estimator are analytically explored. In literature, a lot of work has been done on analyzing
unbiasedness and efficiency of the estimators and more particularly for the population total
estimators. This study departs from these studies by studying the tail properties using the
confidence interval in more detail as opposed to just the unbiasedness, efficiency and mean
squared error. An empirical analysis is done on three artificial functions; linear, quadratic
and exponentially. It is observed that the coverage probabilities from Edgeworth expansion
have higher coverage probabilities compared to design-based Horvitz-Thompson and
Ratio estimators of the finite population total. The Edgeworth expansion also gave a tighter
confidence interval length.
Description
Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, Kenya
Keywords
Asymptotic normality, Coverage Probability, Edgeworth Expansion