Some high-dimensional tests for a one-way MANOVA

Abstract

A statistic is proposed for testing the equality of the mean vectors in a one-way multivariate analysis of variance. The asymptotic null distribution of this statistic, as both the sample size and the number of variables go to infinity, is shown to be normal. Thus, this test can be used when the number of variables is not small relative to the sample size. In particular, it can be used when the number of variables exceeds the degrees of freedom for error, a situation in which standard MANOVA tests are invalid. A related statistic, also having an asymptotic normal distribution, is developed for tests concerning the dimensionality of the hyperplane formed by the population mean vectors. The finite sample size performances of the normal approximations are evaluated in a simulation study.

Nonparametric inference for functional‐on‐scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament

“…However, forming valid tests of various hypotheses about the functional regression parameters, with the control of the error rate, is not straightforward. One solution adopted in the literature is to develop global tests for the parameters of the model (Abramovich & Angelini, 2006;Antoniadis & Sapatinas, 2007;Cardot et al, 2007;Cuesta-Albertos & Febrero-Bande, 2010;Cuevas, Febrero, & Fraiman, 2004;Kayano, Matsui, Yamaguchi, Imoto, & Miyano, 2015;Schott, 2007;Staicu, Li, Crainiceanu, & Ruppert, 2014;Zhang & Liang, 2014). Such tests investigate if a covariate has a significant effect on the response but does not provide any domain selection.…”

A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices

“…For example, among others, Tonda and Fujikoshi [48] obtained the asymptotic null distribution of the likelihood ratio test; Fujikoshi [21] found the asymptotic null distributions for the Lawley-Hotelling trace and the Pillai trace statistics; and Fujikoshi et al [22] considered the Dempster trace test, which is based on the ratio of the trace of the between-class sample covariance matrix to the trace of the within-class sample covariance matrix. Instead of investigating the ratio of the traces of the two sample matrices, Schott [38] proposed a test statistic based on the difference between the traces. Next, we introduce three NTM statistics that are the improvements on T SD , T CQ and T CLX .…”

Test for the mean matrix in a Growth Curve model for high dimensions

“…Srivastava and Fujikoshi (2006) and Srivastava (2007) generalized the test given by Bai and Saranadasa (1996) for two-sample to MANOVA and gave its asymptotic distribution without any assumption on the ratio of convergence of (p/n). Schott (2007) proposed the same test as proposed by Srivastava and Fujikoshi (2006) and Srivastava (2007) but required the assumption that (p/n) → c ∈ (0, ∞) to obtain the asymptotic distribution of the test statistic. This is a severe restriction.…”