Robustness of the triple sampling sequential procedure Seminar

Abstract
In this seminar we discuss the following 1. Historical background of sequential sampling. 2. Triple sampling procedure as presented by Hall (1981) for constructing a fixed width confidence interval for the normal mean with a prescribed coverage. 3. Point estimation for the normal mean. 4. Sensitivity of the sequential normal-based triple sampling procedure for estimating the population mean to departures from normality for underlying distributions. a. Point estimation b. Confidence interval estimation We assume that the underlying population has finite but unknown first four 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 have found that the behaviour of the estimators and the actual sample size depend asymptotically on both the skewness and kurtosis of the underlying distribution. Moreover, the asymptotic regret of using the triple sampling inference instead of the fixed sample size case, had the nuisance parameter been known, is a finite but non-vanishing quantity that depends on the kurtosis of the underlying distribution. The second problem deals with constructing a triple sampling fixed width confidence interval for the unknown population mean with a prescribed width and coverage. The study gives a rigorous account of the sensitivity of the normal-based triple sampling sequential confidence interval for the population when the first four 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, while satisfying Hall?s conditions. Moreover, an asymptotic second order approximation of a differentiable and bounded function of the stopping time is given to calculate the asymptotic coverage based on a second order Edgeworth asymptotic expansion. We found that the asymptotic coverage depends also on the skewness and 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 for the above inferences.