Tolerance Factors in Multiple and Multivariate Linear Regressions

• Activity Number: 309
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Sumona Mondal* and Kalimuthu Krishnamoorthy+
• Companies: Clarkson University and University of Louisiana at Lafayette
• Keywords: Confidence ; Content ; Coverage Probability ; Wishart Distribution ; Wallis' Approximation

Abstract

In this article, an improved method of computing tolerance factors for constructing tolerance regions in a multivariate linear regression model is proposed. The method is based on a chi-square approximation to the distribution of a linear function of noncentral chi-square variables and simulation. The merits of the proposed approach are evaluated using Monte Carlo simulation. The study indicates that the proposed approach is stable and accurate even for small samples, and better than available methods. For constructing two-sided tolerance intervals in multiple linear regression, coverage level adjusted one-sided tolerance factors are shown to be better than available approximate tolerance factors. The results based on the coverage level adjusted one-sided tolerance factors are as good as the ones based on the exact two-sided tolerance factors in many cases.