Powers of some one-sided multivariate tests with the population covariance matrix known up to a multiplicative constant

Obtaining similar null distributions in the normal linear model using computational methods

“…An exception is Follmann's test (Follmann, 1996), although according to Chongcharoen et al (2002) this test is not very powerful. There are other references that do present tests with their finite sample distribution, but for these tests it is assumed that the population covariance matrix is known, or known up to a multiplicative constant (Chongcharoen et al, 2002;Silvapulle, 1995a). Our method provides the similar distribution for any statistic that can be applied to test β = 0 against β * 1 ≥ 0, when the covariance matrix is unknown.…”

One-Sided Multivariate Tests for High Dimensional Data

“…Because the likelihood ratio tests with restricted alternatives are complicated to use, Tang et al (1989) proposed an approximate likelihood ratio test and Follmann (1996) proposed one-sided modifications of the usual χ 2 and Hotelling's T 2 tests of H 0 versus ~H 0 that are easier to implement. Using exact computations and Monte Carlo methods, Chongcharoen et al (2002) compared the performance of Kudo Boyett and Shuster (1977) and the Tang-Gnecco-Geller test for a known covariance matrix and for a partially known covariance matrix, they compared the powers of these tests with Kudo's test replaced by Shorack's test. For a completely unknown covariance matrix, Chongcharoen (2009) studied the power of these one-sided tests for unknown covariance matrices with equal variances and unequal variances as well as tests obtained by combining the Boyett and Shuster (1977) technique to Follmann's test, the new test, Perlman's test and the Tang-Gnecco-Geller test. In some situations, there are no longer data for n>p. That is, when the number n of available observations is smaller than the dimension P of the observed vectors.…”

“…Using exact computations and Monte Carlo methods, Chongcharoen et al (2002) compared the performance of Kudo Boyett and Shuster (1977) and the Tang-Gnecco-Geller test for a known covariance matrix and for a partially known covariance matrix, they compared the powers of these tests with Kudo's test replaced by Shorack's test. For a completely unknown covariance matrix, Chongcharoen (2009) studied the power of these one-sided tests for unknown covariance matrices with equal variances and unequal variances as well as tests obtained by combining the Boyett and Shuster (1977) technique to Follmann's test, the new test, Perlman's test and the Tang-Gnecco-Geller test. In some situations, there are no longer data for n>p. That is, when the number n of available observations is smaller than the dimension P of the observed vectors. For example, the data come from DNA micro arrays where thousands of gene expression levels are measured in relatively few subjects.…”