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Generalized Cramér-von Mises goodness-of-fit tests for multivariate distributions

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  • Chiu, Sung Nok
  • Liu, Kwong Ip

Abstract

A class of statistics for testing the goodness-of-fit for any multivariate continuous distribution is proposed. These statistics consider not only the goodness-of-fit of the joint distribution but also the goodness-of-fit of all marginal distributions, and can be regarded as generalizations of the multivariate Cramér-von Mises statistic. Simulation shows that these generalizations, using the Monte Carlo test procedure to approximate their finite-sample p-values, are more powerful than the multivariate Kolmogorov-Smirnov statistic.

Suggested Citation

  • Chiu, Sung Nok & Liu, Kwong Ip, 2009. "Generalized Cramér-von Mises goodness-of-fit tests for multivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3817-3834, September.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:11:p:3817-3834
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    References listed on IDEAS

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    1. Hickernell, Fred J., 1999. "Goodness-of-fit statistics, discrepancies and robust designs," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 73-78, August.
    2. F. H. C. Marriott, 1979. "Barnard's Monte Carlo Tests: How Many Simulations?," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(1), pages 75-77, March.
    3. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
    4. Bera, A. & John, S., 1983. "Tests for multivariate normality with Pearson alternatives," LIDAM Reprints CORE 534, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    1. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.
    2. Sung Nok Chiu & Kwong Ip Liu, 2013. "Stationarity Tests for Spatial Point Processes using Discrepancies," Biometrics, The International Biometric Society, vol. 69(2), pages 497-507, June.
    3. Yanan Song & Xuejing Zhao, 2021. "Normality Testing of High-Dimensional Data Based on Principle Component and Jarque–Bera Statistics," Stats, MDPI, vol. 4(1), pages 1-12, March.
    4. Cheng, Ching-Wei & Hung, Ying-Chao & Balakrishnan, Narayanaswamy, 2014. "Generating beta random numbers and Dirichlet random vectors in R: The package rBeta2009," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1011-1020.
    5. Langrené, Nicolas & Warin, Xavier, 2021. "Fast multivariate empirical cumulative distribution function with connection to kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    6. Manuel L. Esquível & Nadezhda P. Krasii, 2023. "On Structured Random Matrices Defined by Matrix Substitutions," Mathematics, MDPI, vol. 11(11), pages 1-29, May.
    7. Zhao, Jun & Jang, Yu-Hyeong & Kim, Hyoung-Moon, 2022. "Closed-form and bias-corrected estimators for the bivariate gamma distribution," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    8. Tenreiro, Carlos, 2011. "An affine invariant multiple test procedure for assessing multivariate normality," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1980-1992, May.

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