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Testing the homogeneity of sequences of multivariate Gaussian random variables

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Treść / Zawartość
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Warianty tytułu
PL
Testowanie jednorodności ciągów wielowymiarowych gaussowskich zmiennych losowych
Języki publikacji
EN
Abstrakty
EN
The paper discusses the method of examining the homogeneity of sequences of random variables including testing the normality of multivariate random variables as well as testing the equality of many expected values and testing the equality of many covariance matrices. Some results of application of the method to study the homogeneity of sequences of multivariate Gaussian random variables have been presented.
PL
W pracy omówiono metodę badania jednorodności ciągów wielowymiarowych zmiennych losowych obejmującą badanie normalności rozkładów zmiennych losowych oraz badanie równości wielu wartości oczekiwanych i równości wielu macierzy kowariancji. Przedstawiono przykładowe wyniki zastosowania prezentowanej metody do badania jednorodności ciągów wielowymiarowych gaussowskich zmiennych losowych.
Rocznik
Strony
13--24
Opis fizyczny
Bibliogr. 33 poz., tab.
Twórcy
  • Military University of Technology, Faculty of Cybernetics, Institute of Computer and Information Systems, 2 Kaliskiego Str., 00-908 Warsaw, Poland
Bibliografia
  • [1] Anderson T.W., An Introduction to Multivariate Statistical Analysis, Wiley-Interscience, Hoboken, 2003.
  • [2] Box G.E.P., A General Distribution Theory for a Class of Likelihood Criteria, Biometrika, 36,1949, pp. 317-346.
  • [3] Box G.E.P., Problems in the Analysis of Growth and Wear Curves, Biometrics, 6,1950, pp. 362-389.
  • [4] Box G.E.P., Jenkins G.M., Reinsel G.C., Time Series Analysis: Forecasting and Control, Wiley, Hoboken, 2011.
  • [5] Chenouri S., Small C.G., A Nonparametric Multivariate Multisample Test Based on Data Depth, Electronic Journal of Statistics, vol. 6, 2012, pp. 760-782.
  • [6] Choi K., Marden J., An Approach to Multivariate Rank Tests in Multivariate Analysis of Variance, Journal of the American Statistical Association, vol. 92, no. 440, Dec., 1997, pp. 1581-1590.
  • [7] Desu M.M., Sample Size Methodology, Academic Press, New York, 1990.
  • [8] Epps T.W., Pulley L.B., A Test for Normality Based on the Empirical Characteristic Function, Biometrika 70 (3), 1983, pp. 723-726.
  • [9] Fishman G.S., Discrete-Event Simulation: Modelling, Programming, and Analysis, Springer, New York, 2001.
  • [10] Gentle J.E. (ed.), Hardle W.K. (ed.), MORi Y. (ed.), Handbook of Computational Statistics: Concepts and Methods, Springer, Berlin, 2004.
  • [11] Gonzalez T.F. (ed.), Handbook of Approximation Algorithms and Metaheuristics, Chapman and Hall/CRC, Boca Raton, 2007.
  • [12] Henze N., Zirkler B., A Class of Invariant and Consistent Tests for Multivariate Normality, Communications in Statistics - Theory and Methods 19, Issue 10, 1990, pp. 3595-3617.
  • [13] Henze N„ Wagner T., A New Approach to the BHEP Tests for Multivariate Normality, Journal of Multivariate Analysis, vol. 62, issue 1, July 1997, pp. 1-23.
  • [14] Henze N., Invariant Tests for Multivariate Normality: a Critical Review, Statistical Papers, 43,pp. 467-506.
  • [15] Hotelling H., A Generalized T Test and Measure of Multivariate Dispersion, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1951, University of California Press, Berkeley, pp. 23-41.
  • [16] Kleijnen J.P.C., Design and Analysis of Simulation Experiments, Springer, 2010.
  • [17] Kruskal W.H., A Nonparametric Test for the Several Sample Problem, The Annals of Mathematical Statistics, vol. 23, no. 4, Dec., 1952, pp. 525-540.
  • [18] Kruskal W.H., Wallis W.A., Use of Ranks in One-Criterion Variance Analysis, Journal of the American Statistical Association, vol. 47, no. 260, Dec., 1952, pp. 583-621.
  • [19] Lawley D.N., A Generalization of Fishers z-Test, Biometrika 30,1938, pp. 180-187.
  • [20] Mardia K.V., Measures of Multivariate Skewness and Kurtosis with Applications, Biometrika 57, 1970, pp. 519-530.
  • [21] Mardia K.V., Applications of Some Measures of Multivariate Skewness and Kurtosis in Testing Normality and Robustness Studies, Sankhya: The Indian Journal of Statistics, Series B (1960-2002), vol. 36, no. 2, May, 1974, pp. 115-128.
  • [22] Mardia K.V., Zemroch P.J., Algorithm AS 84: Measures of Multivariate Skewness and Kurtosis, Journal of the Royal Statistical Society, Series C (Applied Statistics), vol. 24, no. 2,1975, pp. 262-265.
  • [23] Mardia K.V., Kent J.T., Bibby J.M., Multivariate Analysis, Academic Press, New York, 1979.
  • [24] Pederzoli G., Rathie P.N., The Exact Distribution of Bartlett’s Criterion for Testing the Equality of Covariance Matrices, Metron. International Journal of Statistics, issue: 3/4, 1983, pp. 83-89.
  • [25] Puri M.L., Sen P.K., Nonparametric Methods in Multivariate Analysis, John Wiley and Sons, New York, 1971.
  • [26] Randles R.H., Peters D., Multivariate Rank Tests for the Two-Sample Location Problem, Communications in Statistics - Theory and Methods, vol. 19, issue 11, 1990, pp. 4225-4238.
  • [27] Romeu J.L., Ozturk A., A Comparative Study of Goodness-of-Fit Tests for Multivariate Normality, Journal of Multivariate Analysis, vol. 46, issue 2, August 1993, pp. 309-334.
  • [28] Royston J.P., Approximating the Shapiro-Wilk W-testfor Non-Normality, Statistics and Computing, 2, 1992, pp. 117-119.
  • [29] Royston J.P., Remark AS R94-. A Remark on Algorithm AS 181: the W Test for Normality, Applied Statistics, 44, 1995, pp. 547-551.
  • [30] Seber G.A.E, Multivariate Observations, New York: John Wiley & Sons, 1984.
  • [31] Szekelya G.J., Rizzob M.L., A New Test for Multivariate Normality, Journal of Multivariate Analysis, vol. 93, issue 1, March 2005, pp. 58-80.
  • [32] Tabachnick B.G., Fidell L.S., Using Multivariate Statistics, Pearson, Harlow, 2013.
  • [33] Um Y., Randles R.H., Nonparametric Tests for the Multivariate Multi-Sample Location Problem, Statistica Sinica, 8, 1998, pp. 801-812.
Uwagi
PL
Publikacja została częściowo sfinansowana przez NCBiR w ramach projektu Nr BI04/006/13143/2013 pt. „Elektroniczny system zarządzania cyklem życia dokumentów o różnych poziomach wrażliwości”.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bb9c7052-22de-473b-993f-10fe05b2e30a
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