Communications for Statistical Applications and Methods

  • 제9권1호
  • /
  • Pages.187-196
  • /
  • 2002
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

The Limit Distribution and Power of a Test for Bivariate Normality

  • 발행 : 2002.04.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Testing for normality has always been a center of practical and theoretical interest in statistical research. In this paper a test statistic for bivariate normality is proposed. The underlying idea is to investigate all the possible linear combinations that reduce to the standard normal distribution under the null hypothesis and compare the order statistics of them with the theoretical normal quantiles. The suggested statistic is invariant with respect to nonsingular matrix multiplication and vector addition. We show that the limit distribution of an approximation to the suggested statistic is represented as the supremum over an index set of the integral of a suitable Gaussian Process. We also simulate the null distribution of the statistic and give some critical values of the distribution and power results.

키워드

참고문헌

  1. Biometrika v.65 Testing multivariate normality Cox, D. R.;Small, N. J. H. https://doi.org/10.1093/biomet/65.2.263
  2. CBMS-NSF regional conference series in applied mathematics Quantile processes with statistical applications Csorgo, M.
  3. Goodness-of-fit Techniques D'Agostino, R. B.;Stephens, M. A.
  4. South African Statistical Journal v.6 Asymptotic distributions of certain test criteria of normality de Wet, T.;Venter, J. H.
  5. The Annals of Statistics v.27 Tests of goodness of fit based on the L₂-Wasserstein distance del Barrio, E.;Cuesta, J. A.;Martran, C.;Rodrlguez, J. M. https://doi.org/10.1214/aos/1017938923
  6. Methods for statistical data analysis of multivariate observations Gnanadesikan, R.
  7. Communications in Statistics - Theory and Methods v.19 A class of invariant and consistent tests for multivariate normality Henze, N.;Zirkler, H. https://doi.org/10.1080/03610929008830400
  8. Journal of Statistical Computation and Simulation v.42 A comparison of tests for multivariate normality that are based on measure of multivariate skewness nad kurtosis Horsewell, R. L.;Looney, S. W. https://doi.org/10.1080/00949659208811407
  9. The Annals of Statistics v.13 Projection pursuti Huber, P. J. https://doi.org/10.1214/aos/1176349519
  10. 한국통계학회논문집 v.4 이변량 정규분포의 적합도 검정을 위한 통계량의 극한분포에 대한 연구 Kim, N.
  11. The Annals of Statistics v.14 Asymptotic distribution of the Shapiro-Wilk W for testing for normality Leslie, J. R.;Stephens, M. A.;Fotopolous, S. https://doi.org/10.1214/aos/1176350172
  12. Biometrika v.70 Two statistics for testing multivariate normality Machado, S. G. https://doi.org/10.1093/biomet/70.3.713
  13. Journal of the American statistical Association v.68 On tests for multivariate normality Malkovich, J. F.;Afifi, A. A. https://doi.org/10.2307/2284163
  14. Biometrika v.57 Measures of multivariate skewness and kurtosis with applications Mardia, K. V. https://doi.org/10.1093/biomet/57.3.519
  15. Sankhya v.A36 Applications of some measures of multivariate skewness and kurtosis for testing normality and robustness studies Mardia, K. V.
  16. Applied Statistics v.24 Assesssment of multivariate normality and the robustness of Hotelling's T² test Mardia, K. V. https://doi.org/10.2307/2346563
  17. In Handbook in Statistics Tests of univariate and multivariate normality Mardia, K. V.;P. R. Krishnaiah(ed.)
  18. Communications in Statistics - Theory and Methods v.12 Omnibus test of multinormality based on skewness and kurtosis Mardia, K. V.;Foster, K. https://doi.org/10.1080/03610928308828452
  19. Journal of the American statistical Association v.67 An approximate analysis of variance test for normality Shapiro, S. S.;Francia, R. S. https://doi.org/10.2307/2284728
  20. Biometrika v.52 An analysis of variance test for normality (complete samples) Shapiro, S. S.;Wilk, M. B. https://doi.org/10.1093/biomet/52.3-4.591