Convexity of Elliptically Contoured Distributions with Applications
Abstract
The problem of evaluating multivariate probabilities arises in many areas of statistics, such as in the construction of confidence regions for the mean vector or regression parameters in a general linear model, the determination of critical regions for certain tests, multiple comparisons, reliability, etc. Because these probabilities are hard to evaluate numberically, a thorough study of the nature of, say, the distribution function is needed to suggest good approximations and inequalities. For example, tables for selected values of parameters are available, and one usually interpolates linearly to get an approximation; if we know that the tabulated function is convex or concave, we also get a bound for the quantity of interest. The Cumulative and rectangular probabilities for elliptically contoured distributions are increasing functions of the correlations, but the rate of increase has not yet been studied. This paper proves some results concerning the convexity in correlations of the distribution functions of random vectors with elliptically contoured distributions, and their absolute values. Sections 2-5 describe the bivariate case, and the last section contains extensions to the multivariate case; the results here are not as strong as for the bivariate case, as the computations are much harder.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 10, 1985
- Accession Number
- ADA163389
Entities
People
- S. Iyengar
- Y. L. Tong
Organizations
- Stanford University