Trimmed A robust analog of hotelling's T2

Abstract

Abstract Hotelling's T2 test for the canonical multivariate problem of testing the significance of a mean vector, and its variations, are known to be variously optimal under the assumption of multivariate normality. However, its shortcomings, when the underlying normality assumption is incorrect, suggest a need for robust procedures. Although, the body of literature on robust estimation is substantial in univariate as well as multivariate settings, the development of robust tests especially in multivariate setting is in relatively rudimentary stages. In this paper, we consider trimming of multivariate samples by coordinates and use the vector of trimmed means so obtained to construct and develop the T 2 test as a robust trimmed means analog of Hotelling's T2. Asymptotic theory in univariate and multivariate settings and Monte Carlo methods are used to construct an approximation for the null distribution of T 2 statistic, and the power function of the test is examined. It is seen that the proposed test provides satisfactory type I error control and substantial gain in power if the underlying population is heavy tailed, and experiences very little loss in power when the population is p-variate normal.