Doctoral Dissertation Defense: Malick Mbodj
Advisor: Dr. Thomas Mathew
Location
Information Technology/Engineering : 456
Date & Time
April 22, 2014, 2:00 pm – 4:00 pm
Description
Title: Ellipsoidal tolerance regions and simultaneous tolerance intervals for some multivariate normal populations
Abstract: A tolerance region for a population is a region computed using a random sample, so as to include a specified proportion or more of the population, with a given confidence level. For computing an ellipsoidal tolerance region for a multivariate normal population, the available approximations are not always satisfactory. The first part of the dissertation is on the development of an accurate approximation for computing the required tolerance factor. This is carried out under an arbitrary unknown covariance matrix, as well as under the intra-class covariance structure. The methodology is extended to the case of a multivariate linear regression model for obtaining an ellipsoidal tolerance region under a fixed set of values of the covariates. The second part of the dissertation is on the derivation of simultaneous tolerance intervals and simultaneous prediction intervals. This is motivated by the fact that an ellipsoidal tolerance region cannot provide information on the distribution of the individual components of the response vector. The derivation of a tolerance rectangle is also investigated under the intra-class covariance structure. Numerical results are given to assess the accuracy of the proposed solutions, and illustrative examples and applications are provided.
Abstract: A tolerance region for a population is a region computed using a random sample, so as to include a specified proportion or more of the population, with a given confidence level. For computing an ellipsoidal tolerance region for a multivariate normal population, the available approximations are not always satisfactory. The first part of the dissertation is on the development of an accurate approximation for computing the required tolerance factor. This is carried out under an arbitrary unknown covariance matrix, as well as under the intra-class covariance structure. The methodology is extended to the case of a multivariate linear regression model for obtaining an ellipsoidal tolerance region under a fixed set of values of the covariates. The second part of the dissertation is on the derivation of simultaneous tolerance intervals and simultaneous prediction intervals. This is motivated by the fact that an ellipsoidal tolerance region cannot provide information on the distribution of the individual components of the response vector. The derivation of a tolerance rectangle is also investigated under the intra-class covariance structure. Numerical results are given to assess the accuracy of the proposed solutions, and illustrative examples and applications are provided.
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