Abstract
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 of i.i.d. uniform rv's. These transformations can be used to construct goodness-of-fit tests for these multivariate normal distributions. Two examples are given to illustrate the application of these tests to numerical problems.
Citation
S. Rincon-Gallardo. C. P. Quesenberry. Federico J. O'Reilly. "Conditional Probability Integral Transformations and Goodness-of-Fit Tests for Multivariate Normal Distributions." Ann. Statist. 7 (5) 1052 - 1057, September, 1979. https://doi.org/10.1214/aos/1176344788
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