A test for the mean vector with fewer observations than the dimension under non-normality

47Citations
Citations of this article
28Readers
Mendeley users who have this article in their library.

Abstract

In this article, we consider the problem of testing that the mean vector μ = 0 in the model xj = μ + C zj, j = 1, ..., N, where zj are random p-vectors, zj = (zi j, ..., zp j)′ and zi j are independently and identically distributed with finite four moments, i = 1, ..., p, j = 1, ..., N; that is xi need not be normally distributed. We shall assume that C is a p × p non-singular matrix, and there are fewer observations than the dimension, N ≤ p. We consider the test statistic T = [N over(x, -)′ Ds- 1 over(x, -) - n p / (n - 2)] / [2 tr R2 - p2 / n]frac(1, 2), where over(x, -) is the sample mean vector, S = (si j) is the sample covariance matrix, DS = diag (s11, ..., sp p), R = Ds- frac(1, 2) S Ds- frac(1, 2) and n = N - 1. The asymptotic null and non-null distributions of the test statistic T are derived. © 2008.

Cite

CITATION STYLE

APA

Srivastava, M. S. (2009). A test for the mean vector with fewer observations than the dimension under non-normality. Journal of Multivariate Analysis, 100(3), 518–532. https://doi.org/10.1016/j.jmva.2008.06.006

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free