Date of Completion

8-21-2013

Embargo Period

8-21-2013

Keywords

Sequential, Confidence Regions, Multiple Crossing

Major Advisor

Nitis Mukhopadhyay

Associate Advisor

Joseph Glaz

Associate Advisor

Ofer Harel

Field of Study

Statistics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

This dissertation introduces a novel sequential sampling methodology. The strategy for termination associated with this methodology is called multiple crossing stopping rule. Properties of the multiple crossing stopping rule are illustrated analytically as well as by simulations. Comparisons are made between the multiple crossing methodology and some of the existing methodologies, and relative merits are discussed. First, the proposed methodology is discussed in the context of estimating the mean of a normal population with a fixed-width confidence interval. Efficiency, and asymptotic consistency of the multiple crossing methodology is proven. The coverage probabilities are discussed by the means of extensive simulations. A truncation technique is proposed to improve the implementation. A real data implementation of the proposed methodology is discussed with respect to the gas mileage estimates of new vehicle models provided by the Environment Protection Agency (EPA). Next, the multiple crossing methodology is developed to estimate the mean vector of a multivariate normal distribution. Motivation for the proposed methodology is presented by extending a theoretical result by Simons (1968) to the multivariate normal context. A fine-tuned adjustment along the lines of Mukhopadhyay and Datta (1995) is proposed which improves practical implementation remarkably. A software benchmarking exercise based on multiple crossing sequential sampling is illustrated under real-time data gathering . Finally, regression parameters are estimated by a fixed-size confidence region, wherein sampling is based on the multiple crossing methodology. Important theoretical properties are proven. Some characteristics are discussed with the use of simulations. A truncation technique as well as a fine-tuned adjustment is proposed to improve practical usefulness. We conclude by emphasizing that the multiple crossing methodology is a versatile technique that may be easily applied to a variety of other outstanding problems in point estimation, hypothesis testing, and selection and ranking. It may also be extended to analogous problems arising from non-normal populations.

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