Empirical likelihood confidence intervals for adaptive cluster sampling


Salehi, Mohammad, Mohammadi, Mohammad, Rao, J.N.K. and Berger, Yves G. (2010) Empirical likelihood confidence intervals for adaptive cluster sampling. Environmental and Ecological Statistics, 17, (1), Spring Issue, 111-123. (doi:10.1007/s10651-008-0105-9).

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Description/Abstract

Adaptive cluster sampling (ACS) is an efficient sampling design for estimating parameters of rare and clustered populations. It is widely used in ecological research. The modified Hansen-Hurwitz (HH) and Horvitz-Thompson (HT) estimators based on small samples under ACS have often highly skewed distributions. In such situations, confidence intervals based on traditional normal approximation can lead to unsatisfactory results, with poor coverage properties. Christman and Pontius (Biometrics 56:503–510, 2000) showed that bootstrap percentile methods are appropriate for constructing confidence intervals from the HH estimator. But Perez and Pontius (J Stat Comput Simul 76:755–764, 2006) showed that bootstrap confidence intervals from the HT estimator are even worse than the normal approximation confidence intervals. In this article, we consider two pseudo empirical likelihood functions under the ACS design. One leads to the HH estimator and the other leads to a HT type estimator known as the Hájek estimator. Based on these two empirical likelihood functions, we derive confidence intervals for the population mean. Using a simulation study, we show that the confidence intervals obtained from the first EL function perform as good as the bootstrap confidence intervals from the HH estimator but the confidence intervals obtained from the second EL function perform much better than the bootstrap confidence intervals from the HT estimator, in terms of coverage rate.

Item Type: Article
ISSNs: 1352-8505 (print)
1573-3009 (electronic)
Keywords: finite population, hansen-hurwitz estimator, horvitz-thompson estimator, empirical likelihood ratio
Subjects: H Social Sciences > HA Statistics
Divisions: University Structure - Pre August 2011 > Southampton Statistical Sciences Research Institute
ePrint ID: 159345
Date Deposited: 29 Jun 2010 15:20
Last Modified: 27 Mar 2014 19:15
URI: http://eprints.soton.ac.uk/id/eprint/159345

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