TITLE: Tolerance Limits for Binary Data Under Logistic Regression

SPEAKER: Thomas Mathew

ABSTRACT:

Tolerance limits computed using a random sample capture a specified proportion or more of a population, with a given confidence level. In the talk, the computation of tolerance limits will be discussed for binary data under the logistic regression model. The data consist of n binary responses, where the probability of a positive response depends on covariates via the logistic regression function. Upper tolerance limits are constructed for the number of positive responses in m future trials for fixed as well as for varying levels of the covariates. The former provides point-wise upper tolerance limits, and the latter provides simultaneous upper tolerance limits. The upper tolerance limits are obtained from upper confidence limits for the probability of a positive response. To compute the required upper confidence limits for the

logistic function, likelihood based asymptotic methods, small sample asymptotics, as well as bootstrap methods will be discussed and numerically compared. The problems have been motivated by an application of interest to the U.S. Army, dealing with the testing of ballistic vests for protecting soldiers from projectiles and shrapnel, where the success probability depends on covariates such as the projectile velocity, size of the vest, etc. Such an application will be used to motivate and illustrate the tolerance limit problem.

The talk is based on joint work with Zachary Zimmer and DoHwan Park.

BIO: Thomas Mathew is Professor, Department of Mathematics and Statistics, University of Maryland, Baltimore County Campus. He received his PhD in statistics from the Indian Statistical Institute in 1983. His research interests include the topics of equivalence testing and statistical tolerance intervals. He is the co-author of a Wiley book on tolerance intervals, published in 2009. He is a Fellow of both the Institute of Mathematical Statistics and the American Statistical Association.