A Goodness-of-Fit Test for Multivariate Normal Distribution Using Modified Squared Distance Yim, Mi-Hong; Park, Hyun-Jung; Kim, Joo-Han;
The goodness-of-fit test for multivariate normal distribution is important because most multivariate statistical methods are based on the assumption of multivariate normality. We propose goodness-of-fit test statistics for multivariate normality based on the modified squared distance. The empirical percentage points of the null distribution of the proposed statistics are presented via numerical simulations. We compare performance of several test statistics through a Monte Carlo simulation.
Multivariate normal distribution;goodness-of-fit test;empirical distribution function;modified squared distance;
Fattorini, L. (1986). Remarks on the use of the Shapiro-Wilk test statistics for testing multivariate normality, Statistica(Bologna), 46, 209-217.
Hawkins, D. M. (1981). A new test for multivariate normality and homoscedasticity, Technometrics, 23, 105-110.
Koziol, J. A. (1982). A class of invariant procedures for assessing multivariate normality, Biometrika, 69, 423-427.
Malkovich, J. F. and Afifi, A. A. (1973). On tests for multivariate normality, Journal of the American Statistical Association, 68, 176-179.
Moore, D. S. and Stubblebine, J. B. (1981). Chi-square tests for multivariate normality with application to common stock prices, Communications in Statistics - Theory and Methods, 10, 713-738.
Paulson, A. S., Roohan, P. and Sullo, P. (1987). Some empirical distribution function tests for multivariate normality, Journal of Statistical Computation Simulation, 28, 15-30.
Shapiro, S. S. and Wilk, M. B. (1965). An analysis of variance test for normality(Complete sample), Biometrika, 52(3 and 4), 591-611.
Tsai, K. T. and Koziol, J. A. (1988). A correlation type procedure for assessing multivariate normality, Communications in Statistics - Simulation and Computation, 17, 637-651.
Yim, M. H. (2012). A Goodness-of-Fit Test for Multivariate Normal Distribution, PhD Thesis, Chungnam National University.