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Volumn 75, Issue 2, 2005, Pages 93-107

A Monte Carlo comparison of the Type I and Type II error rates of tests of multivariate normality

Author keywords

Empirical characteristic function; Goodness of fit; Mardia's skewness and kurtosis; Power comparison

Indexed keywords


EID: 27844466678     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/0094965042000193233     Document Type: Article
Times cited : (89)

References (55)
  • 1
    • 3042540974 scopus 로고
    • How to use tests for univariate normality to assess multivariate normality
    • Looney, S., 1995, How to use tests for univariate normality to assess multivariate normality. The American Statistician, 39, 75-79.
    • (1995) The American Statistician , vol.39 , pp. 75-79
    • Looney, S.1
  • 3
    • 0001521368 scopus 로고    scopus 로고
    • On the meaning and use of kurtosis
    • DeCarlo, L., 1997, On the meaning and use of kurtosis. Psychological Methods, 2, 292-307.
    • (1997) Psychological Methods , vol.2 , pp. 292-307
    • DeCarlo, L.1
  • 7
    • 2942611661 scopus 로고
    • Measures of multivariate skewness and kurtosis with applications
    • Mardia, K., 1970, Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519-530.
    • (1970) Biometrika , vol.57 , pp. 519-530
    • Mardia, K.1
  • 8
    • 0000182707 scopus 로고
    • A class of invariant procedures for assessing multivariate normality
    • Koziol, J., 1982, A class of invariant procedures for assessing multivariate normality. Biometrika, 69, 423-427.
    • (1982) Biometrika , vol.69 , pp. 423-427
    • Koziol, J.1
  • 10
    • 0001219270 scopus 로고
    • Rao score tests for goodness of fit and independence
    • Mardia, K. and Kent, J., 1991, Rao score tests for goodness of fit and independence. Biometrika, 78, 355-363.
    • (1991) Biometrika , vol.78 , pp. 355-363
    • Mardia, K.1    Kent, J.2
  • 11
    • 0000061805 scopus 로고
    • Probability plots for assessing multivariate normality
    • Koziol, J., 1993, Probability plots for assessing multivariate normality. The Statistician, 42, 161-174.
    • (1993) The Statistician , vol.42 , pp. 161-174
    • Koziol, J.1
  • 12
    • 0010914214 scopus 로고
    • Marginal skewness and kurtosis in testing multivariate normality
    • Small, N., 1980, Marginal skewness and kurtosis in testing multivariate normality. Applied Statistics, 29, 85-87.
    • (1980) Applied Statistics , vol.29 , pp. 85-87
    • Small, N.1
  • 13
    • 0020984686 scopus 로고
    • Some techniques for assessing multivariate normality based on the Shapiro-Wilk w
    • Royston, J., 1983, Some techniques for assessing multivariate normality based on the Shapiro-Wilk w. Applied Statistics, 32, 121-133.
    • (1983) Applied Statistics , vol.32 , pp. 121-133
    • Royston, J.1
  • 14
    • 0000903755 scopus 로고
    • A consistent test for multivariate normality
    • Baringhaus, L. and Henze, N., 1988, A consistent test for multivariate normality. Metrika, 35, 339-348.
    • (1988) Metrika , vol.35 , pp. 339-348
    • Baringhaus, L.1    Henze, N.2
  • 17
    • 70350340104 scopus 로고
    • Tests of univariate and multivariate normality
    • P.R. Krishnaiah (Ed.) (Amsterdam: North Holland)
    • Mardia, K., 1980, Tests of univariate and multivariate normality. In: P.R. Krishnaiah (Ed.) Handbook of Statistics, Vol. 1 (Amsterdam: North Holland), pp. 297-320.
    • (1980) Handbook of Statistics , vol.1 , pp. 297-320
    • Mardia, K.1
  • 19
    • 0036823683 scopus 로고    scopus 로고
    • Invariant tests for multivariate normality: A critical review
    • Henze, N., 2002, Invariant tests for multivariate normality: a critical review. Statistical Papers, 43, 467-503.
    • (2002) Statistical Papers , vol.43 , pp. 467-503
    • Henze, N.1
  • 20
    • 3042587293 scopus 로고    scopus 로고
    • An appraisal and bibliography of tests for multivariate normality
    • Mecklin, C. and Mundfrom, D., 2004, An appraisal and bibliography of tests for multivariate normality. International Statistical Review, 72, 123-138.
    • (2004) International Statistical Review , vol.72 , pp. 123-138
    • Mecklin, C.1    Mundfrom, D.2
  • 23
    • 0002137108 scopus 로고
    • A comparison of tests for multivariate normality that are based on measures of multivariate skewness and kurtosis
    • Horswell, R. and Looney, S., 1992, A comparison of tests for multivariate normality that are based on measures of multivariate skewness and kurtosis. Journal of Statistical Computation and Simulation, 42, 21-38.
    • (1992) Journal of Statistical Computation and Simulation , vol.42 , pp. 21-38
    • Horswell, R.1    Looney, S.2
  • 24
    • 0002536134 scopus 로고
    • A comparative study of goodness-of-fit tests for multivariate normality
    • Romeu, J. and Ozturk, A., 1993, A comparative study of goodness-of-fit tests for multivariate normality. Journal of Multivariate Analysis, 46, 309-334.
    • (1993) Journal of Multivariate Analysis , vol.46 , pp. 309-334
    • Romeu, J.1    Ozturk, A.2
  • 25
    • 0029106010 scopus 로고
    • A comparison of six test statistics for detecting multivariate nonnormality which utilize the multivariate squared-radii statistic
    • Young, D., Seaman, S. and Seaman, J., 1995, A comparison of six test statistics for detecting multivariate nonnormality which utilize the multivariate squared-radii statistic. Texas Journal of Science, 47, 21-38.
    • (1995) Texas Journal of Science , vol.47 , pp. 21-38
    • Young, D.1    Seaman, S.2    Seaman, J.3
  • 26
    • 0003065638 scopus 로고    scopus 로고
    • Data driven smooth tests for bivariate normality
    • Bogdan, M., 1999, Data driven smooth tests for bivariate normality. Journal of Multivariate Analysis, 68, 26-52.
    • (1999) Journal of Multivariate Analysis , vol.68 , pp. 26-52
    • Bogdan, M.1
  • 28
    • 0000485584 scopus 로고
    • Consistency of some tests for multivariate normality
    • Csörgö, S., 1989, Consistency of some tests for multivariate normality. Metrika, 36, 107-116.
    • (1989) Metrika , vol.36 , pp. 107-116
    • Csörgö, S.1
  • 29
    • 0000073309 scopus 로고
    • Multivariate normal plotting
    • Healy, M., 1968, Multivariate normal plotting. Applied Statistics, 17, 157-161.
    • (1968) Applied Statistics , vol.17 , pp. 157-161
    • Healy, M.1
  • 30
    • 0002954125 scopus 로고
    • Robust estimates, residuals, and outlier detection with multiresponse data
    • Gnanadesikan, R. and Kettenring, J., 1972, Robust estimates, residuals, and outlier detection with multiresponse data. Biometrics, 28, 81-124.
    • (1972) Biometrics , vol.28 , pp. 81-124
    • Gnanadesikan, R.1    Kettenring, J.2
  • 31
    • 0018071299 scopus 로고
    • Plotting squared radii
    • Small, N., 1978, Plotting squared radii. Biometrika, 65, 657-658.
    • (1978) Biometrika , vol.65 , pp. 657-658
    • Small, N.1
  • 32
    • 0001243428 scopus 로고
    • Omnibus robust procedures for assessment of multivariate normality and detection of multivariate outliers
    • G.P. Patil and C.R. Rao (Eds) (Amsterdam: North Holland)
    • Singh, A., 1993, Omnibus robust procedures for assessment of multivariate normality and detection of multivariate outliers. In: G.P. Patil and C.R. Rao (Eds) Multivariate Environmental Statistics (Amsterdam: North Holland), pp. 445-488.
    • (1993) Multivariate Environmental Statistics , pp. 445-488
    • Singh, A.1
  • 33
    • 0002063041 scopus 로고
    • Robust m-estimators of multivariate location and scatter
    • Maronna, R., 1976, Robust m-estimators of multivariate location and scatter. Annals of Statistics, 4, 51-67.
    • (1976) Annals of Statistics , vol.4 , pp. 51-67
    • Maronna, R.1
  • 34
    • 84963473486 scopus 로고
    • Omnibus tests of multinormality based on skewness and kurtosis
    • Mardia, K. and Foster, K., 1983, Omnibus tests of multinormality based on skewness and kurtosis. Communications in Statistics, 12, 207-221.
    • (1983) Communications in Statistics , vol.12 , pp. 207-221
    • Mardia, K.1    Foster, K.2
  • 35
    • 0001934955 scopus 로고
    • A new test for multivariate normality and homoscedasticity
    • Hawkins, D., 1981, A new test for multivariate normality and homoscedasticity. Technometrics, 23, 105-110.
    • (1981) Technometrics , vol.23 , pp. 105-110
    • Hawkins, D.1
  • 37
    • 0000898845 scopus 로고
    • An analysis of variance test for normality
    • Shapiro, S. and Wilk, M., 1965, An analysis of variance test for normality. Biometrika, 52, 591-611.
    • (1965) Biometrika , vol.52 , pp. 591-611
    • Shapiro, S.1    Wilk, M.2
  • 39
    • 84985657527 scopus 로고
    • A new statistical goodness-of-fit test based on graphical representation
    • Ozturk, A. and Dudewicz, E., 1992, A new statistical goodness-of-fit test based on graphical representation. Biometrical Journal, 34, 403-427.
    • (1992) Biometrical Journal , vol.34 , pp. 403-427
    • Ozturk, A.1    Dudewicz, E.2
  • 42
    • 0001623560 scopus 로고
    • A test for normality based on the empirical characteristic function
    • Epps, T. and Pulley, L., 1983, A test for normality based on the empirical characteristic function. Biometrika, 70, 723-726.
    • (1983) Biometrika , vol.70 , pp. 723-726
    • Epps, T.1    Pulley, L.2
  • 43
    • 0000415646 scopus 로고
    • Testing for normality in arbitrary dimension
    • Csörgö, S., 1986, Testing for normality in arbitrary dimension. Annals of Statistics, 14, 708-723.
    • (1986) Annals of Statistics , vol.14 , pp. 708-723
    • Csörgö, S.1
  • 44
    • 21144470310 scopus 로고
    • Adaptive smoothing and density based tests of multivariate normality
    • Bowman, A. and Foster, P., 1993, Adaptive smoothing and density based tests of multivariate normality. Journal of the American Statistical Association, 88, 529-537.
    • (1993) Journal of the American Statistical Association , vol.88 , pp. 529-537
    • Bowman, A.1    Foster, P.2
  • 45
    • 0031572681 scopus 로고    scopus 로고
    • Extreme smoothing and testing for multivariate normality
    • Henze, N., 1997, Extreme smoothing and testing for multivariate normality. Statistics and Probability Letters 35, 203-213.
    • (1997) Statistics and Probability Letters , vol.35 , pp. 203-213
    • Henze, N.1
  • 46
    • 0031185197 scopus 로고    scopus 로고
    • A new approach to the BHEP tests for multivariate normality
    • Henze, N. and Wagner, T., 1997, A new approach to the BHEP tests for multivariate normality. Journal of Multivariate Analysis, 62, 1-23.
    • (1997) Journal of Multivariate Analysis , vol.62 , pp. 1-23
    • Henze, N.1    Wagner, T.2
  • 47
    • 84988122986 scopus 로고
    • Applications of empirical characteristic functions in some multivariate problems
    • Ghosh, S. and Ruymgaart, F., 1992, Applications of empirical characteristic functions in some multivariate problems. Canadian Journal of Statistics, 20, 429-440.
    • (1992) Canadian Journal of Statistics , vol.20 , pp. 429-440
    • Ghosh, S.1    Ruymgaart, F.2
  • 48
    • 0000190321 scopus 로고    scopus 로고
    • On weighting the studentized empirical characteristic function for testing normality
    • Naito, K., 1996, On weighting the studentized empirical characteristic function for testing normality. Communications in Statistics: Computation and Simulation, 25, 201-213.
    • (1996) Communications in Statistics: Computation and Simulation , vol.25 , pp. 201-213
    • Naito, K.1
  • 49
    • 21144466927 scopus 로고
    • Limit distributions for Mardia's measure of multivariate skewness
    • Baringhaus, L. and Henze, N., 1992, Limit distributions for Mardia's measure of multivariate skewness. Annals of Statistics, 20, 1889-1902.
    • (1992) Annals of Statistics , vol.20 , pp. 1889-1902
    • Baringhaus, L.1    Henze, N.2
  • 50
  • 53
    • 27844603111 scopus 로고    scopus 로고
    • Testing for model fit: Assessing box-cox transformations of data to near normality
    • Bozdogan, H. and Ramirez, D., 1997, Testing for model fit: Assessing box-cox transformations of data to near normality. Computational Statistics Quarterly, 3, 203-213.
    • (1997) Computational Statistics Quarterly , vol.3 , pp. 203-213
    • Bozdogan, H.1    Ramirez, D.2
  • 54
    • 0013038230 scopus 로고
    • Locally best invariant tests for multivariate normality
    • Kariya, T. and George, E., 1995, Locally best invariant tests for multivariate normality. Sankhya, 57, 440-51.
    • (1995) Sankhya , vol.57 , pp. 440-451
    • Kariya, T.1    George, E.2
  • 55
    • 38249035999 scopus 로고
    • On assessing multivariate normality based on Shapiro-Wilk w statistic
    • Srivastava, M. and Hui, T., 1987, On assessing multivariate normality based on Shapiro-Wilk w statistic. Statistics and Probability Letters, 5, 15-18.
    • (1987) Statistics and Probability Letters , vol.5 , pp. 15-18
    • Srivastava, M.1    Hui, T.2


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