References
- Arcones, M. A. (2007). Two tests for multivariate normality based on the characteristic function. Mathematical Methods of Statistics 16:177–201.
- Baringhaus, L., Henze, N. (1988). A consistent test for multivariate normality based on the empirical characteristic function. Metrika 35:339–348.
- Baringhaus, L., Henze, N. (1992). Limit distributions for Mardia’s measure of multivariate skewness. Annals of Statistics 20:1889–1902.
- Beirlant, J., Mason, D. M., Vynckier, C. (1999). Goodness-of-fit analysis for multivariate normality based on generalized quantiles. Computational Statistics & Data Analysis 30:119–142.
- Bowman, A. W., Foster, P. J. (1993). Adaptive smoothing and density-based tests of multivariate normality. Journal of American Statistical Association 88:529–537.
- Chiu, S. N., Liu, K. I. (2009). Generalized Cramér-von Mises goodness-of-fit tests for multivariate distributions. Computational Statistics & Data Analysis 53:3817–3834.
- Csörgő, S. (1986). Testing for normality in arbitrary dimension. Annals of Statistics 14:708–723.
- Csörgő, S. (1989). Consistency of some tests for multivariate normality. Metrika 36:107–116.
- Dykstra, R. L. (1970). Establishing the positive definiteness of the sample covariance matrix. The Annals of Mathematical Statistics 41:2153–2154.
- Ebner, B. (2012). Asymptotic theory for the test for multivariate normality by Cox and Small. Journal of Multivariate Analysis 111:368–379.
- Epps, T. W., Pulley, L. B. (1983). A test for normality based on the empirical characteristic function. Biometrika 70:723–726.
- Fan, Y. (1998). Goodness-of-fit tests based on kernel density estimators with fixed smoothing parameters. Econometric Theory 14:604–621.
- Farrel, P. J., Salibian-Barrera, M., Naczk, K. (2007). On tests for multivariate normality and associated simulation studies. Journal of Statistical Computation and Simulation 77:1065–1080.
- Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics 7:179–188.
- Fromont, M., Laurent, B. (2006). Adaptive goodness-of-fit tests in a density model. Annals of Statistics 34:680–720.
- Gürtler, N. (2000). Asymptotic Theorems for the Class of BHEP-Tests for Multivariate Normality with Fixed and Variable Smoothing Parameter (in German). Ph.D. dissertation, Germany: University of Karlsruhe.
- Henze, N. (1997). Extreme smoothing and testing for multivariate normality. Statistics & Probability Letters 35:203–213.
- Henze, N. (2002). Invariant tests for multivariate normality: A critical review. Statistical Papers 43:467–506.
- Henze, N., Wagner, T. (1997). A new approach to the BHEP tests for multivariate normality. Journal of Multivariate Analysis 62:1–23.
- Henze, N., Zirkler, B. (1990). A class of invariant consistent tests for multivariate normality. Communications in Statistics - Theory and Methods 19:3595–3617.
- Johnson, M. E. (1987). Multivariate Statistical Simulation. New York: Wiley.
- Kotz, S., Kozubowski, T., Podgorski, K. (2001). The Laplace Distribution and Generalizations. Boston, MA: Birkhauser.
- Liang, J., Pan, W. S. Y., Yang, Z.-H. (2005). Characterization-based Q-Q plots for testing multinormality. Statistics & Probability Letters 70:183–190.
- Liang, J., Tang, M.-L., Chan, P. S. (2009). A generalized Shapiro–Wilk W statistic for testing high-dimensional normality. Computational Statistics & Data Analysis 53:3883–3891.
- Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika 57:519–530.
- Mecklin, C. J., Mundfrom, D. J. (2004). An appraisal and bibliography of tests for multivariate normality. International Statistical Review 72:123–138.
- Mecklin, C. J., Mundfrom, D. J. (2005). A Monte Carlo comparison of Type I and Type II error rates of tests of multivariate normality. Journal of Statistical Computation and Simulation 75:93–107.
- Móri, T. F., Rohatgi, V. K., Székely, G. J. (1993). On multivariate skewness and kurtosis. Theory of Probability and Its Applications 38:547–551.
- Oliveira, I. R. C., Ferreira, D. F. (2010). Multivariate extension of chi-squared univariate normality test. Journal of Statistical Computation and Simulation 80:513–526.
- Ramberg, J. S., Schmeiser, B. W. (1974). An approximate method for generating asymmetric random variables. Communications of the ACM 17:78–82.
- Rayner, J. C. W., Best, D. J. (1989). Smooth Tests of Goodness of Fit. New York: Oxford University Press.
- R Development Core Team, (2011). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Available at: http://www.R-project.org
- Romeu, J. L., Ozturk, A. (1993). A comparative study of goodness-of-fit tests for multivariate normality. Journal of Multivariate Analysis 46:309–334.
- Shorack, G. R., Wellner, J. A. (1986). Empirical Processes with Applications to Statistics. New York: Wiley.
- Small, N. J. H. (1980). Marginal skewness and kurtosis in testing multivariate normality. Journal of the Royal Statistical Society, Series C 29:85–87.
- Sürücü, B. (2006). Goodness-of-fit tests for multivariate distributions. Communications in Statistics - Theory and Methods 35:1319–1331.
- Székely, G. J., Rizzo, M. L. (2005). A new test for multivariate normality. Journal of Multivariate Analysis 93:58–80.
- Tenreiro, C. (2007). On the asymptotic behaviour of location-scale invariant Bickel-Rosenblatt tests. Journal of Statistical Planning and Inference 137:103–116. Erratum: 139:2115 (2009).
- Tenreiro, C. (2009). On the choice of the smoothing parameter for the BHEP goodness-of-fit test. Computational Statistics & Data Analysis 53:1038–1053.
- Tenreiro, C. (2011). An affine invariant multiple test procedure for assessing multivariate normality. Computational Statistics & Data Analysis 55:1980–1992.
- Thode, Jr., H. C. (2002). Testing for Normality. New York: Marcel Dekker.
- Wang, C.-C. (2015). A MATLAB package for multivariate normality test. Journal of Statistical Computation and Simulation 85:166–188.