2015/12/30 by Peter D. Hoff, Hoff, Peter D. · 1 citation
Mathematics · #62H15 #Advanced Statistical Methods and Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1512.09020
openalex publication_date 2015/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Many inference techniques for multivariate data analysis assume that the rows\nof the data matrix are realizations of independent and identically distributed\nrandom vectors. Such an assumption will be met, for example, if the rows of the\ndata matrix are multivariate measurements on a set of independently sampled\nunits. In the absence of an independent random sample, a relevant question is\nwhether or not a statistical model that assumes such row exchangeability is\nplausible. One method for assessing this plausibility is a statistical test of\nrow covariation. Maintenance of a constant type I error rate regardless of the\ncolumn covariance or matrix mean can be accomplished with a test that is\ninvariant under an appropriate group of transformations. In the context of a\nclass of elliptically contoured matrix regression models (such as matrix normal\nmodels), I show that there are no non-trivial invariant tests if the number of\nrows is not sufficiently larger than the number of columns. Furthermore, I show\nthat even if the number of rows is large, there are no non-trivial invariant\ntests that have power to detect arbitrary row covariance in the presence of\narbitrary column covariance. However, we can construct biased tests that have\npower to detect certain types of row covariance that may be encountered in\npractice.\n