Conditional Probability Integral Transformations and Goodness-of-Fit Tests for Multivariate Normal Distributions
Conditional Probability Integral Transformations and Goodness-of-Fit Tests for Multivariate Normal Distributions
Let $X_1, \cdots, X_n$ be a random sample from a full-rank multivariate normal distribution $N(\mu, \Sigma)$. The two cases (i) $\mu$ unknown and $\Sigma = \sigma^2\Sigma_0, \Sigma_0$ known, and (ii) $\mu$ and $\Sigma$ completely unknown are considered here. Transformations are given that transform the observation vectors to a (smaller) set …