Distribution Results for Positive Definite Quadratic Forms with Repeated Roots

摘要

The distribution of a statistic which is a positive linear combination of independent chi-square random variables is evaluated in certain cases where some of the degrees of freedom are larger than one. Such statistics arise in positive definite quadratic forms of normal random vectors and as the trace of a Wishart matrix. They also arise in the asymptotic distribution for chi-squared goodness-of-fit tests with estimated parameters and for the average Kendall tau statistic. (Author)