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Title: Robustness of triple sampling inference procedures to underlying distributions
Author: Yousef, Ali Saleh Ali
Awarding Body: University of Southampton
Current Institution: University of Southampton
Date of Award: 2010
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In this study, the sensitivity of the sequential normal-based triple sampling procedure for estimating the population mean to departures from normality is discussed. We assume only that the underlying population has finite but unknown first six moments. Two main inferential methodologies are considered. First point estimation of the unknown population mean is investigated where a squared error loss function with linear sampling cost is assumed to control the risk of estimating the unknown population mean by the corresponding sample measure. We find that the behaviour of the estimators and of the sample size depends asymptotically on both the skewness and kurtosis of the underlying distribution and we quantify this dependence. Moreover, the asymptotic regret of using the triple sampling inference instead of the fixed sample size approach, had the nuisance parameter been known, is a finite but non-vanishing quantity that depends on the kurtosis of the underlying distribution. We also supplement our findings with a simulation experiment to study the performance of the estimators and the sample size in a range of conditions and compare the asymptotic and finite sample results. The second part of the thesis deals with constructing a triple sampling fixed width confidence interval for the unknown population mean with a prescribed width and coverage while protecting the interval against Type II error. An account is given of the sensitivity of the normal-based triple sampling sequential confidence interval for the population when the first six moments are assumed to exist but are unknown. First, triple sampling sequential confidence intervals for the mean are constructed using Hall’s (1981) methodology. Hence asymptotic characteristics of the constructed interval are discussed and justified. Then an asymptotic second order approximation of a continuously differentiable and bounded function of the stopping time is given to calculate both asymptotic coverage based on a second order Edgeworth asymptotic expansion and the Type II error probability. The impact of several parameters on the Type II error probability is explored for various continuous distributions. Finally, a simulation experiment is performed to investigate the methods in finite sample cases and to compare the finite sample and asymptotic results.
Supervisor: Kimber, Alan Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics