Sensitivity of normal-based triple sampling sequential point estimation to the normality assumption |
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Authors: | AS Yousef AC Kimber HI Hamdy |
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Institution: | 1. University of Southampton, School of Mathematics and Southampton Statistical Sciences Research Institute, Highfield Campus, Southampton SO17 1BJ, United Kingdom;2. Kuwait University, Kuwait |
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Abstract: | This paper discusses the sensitivity of the sequential normal-based triple sampling procedure for estimating the population mean to departures from normality. We assume that the underlying population has finite absolute sixth moment and find that asymptotically the behavior of the estimator and of the sample size depend on the skewness and kurtosis of the underlying distribution when using a squared error loss function with linear sampling cost. These results enable the effects of non-normality easily to be assessed both qualitatively and quantitatively. We supplement our asymptotic results with a simulation experiment to study the performance of the estimator and the sample size in a range of conditions. |
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Keywords: | Asymptotic relative efficiency Kurtosis Regret Sampling cost Simulation Skewness Squared error loss function Taylor expansion |
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