Commenced in January 2007
Paper Count: 31738
Distribution Sampling of Vector Variance without Duplications
Abstract:In recent years, the use of vector variance as a measure of multivariate variability has received much attention in wide range of statistics. This paper deals with a more economic measure of multivariate variability, defined as vector variance minus all duplication elements. For high dimensional data, this will increase the computational efficiency almost 50 % compared to the original vector variance. Its sampling distribution will be investigated to make its applications possible.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1057275Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1355
 F.B. Alt, and N.D. Smith Multivariate process control. In: Krishnaiah, P.R., Rao, C.R., eds. Handbook of Statistics, Vo. 7 Elsevier Sciences Publishers, 1988, pp. 333-351.
 M.J. Anderson, Distance based test for homogeneity of multivariate dispersion, Biometrics, 62, 2006. 245 -253.
 T.W. Anderson, An Introduction to multivariate statistical analysis. John Wiley & Sons, Inc., New York. 1958.
 J. Ng. R Chilson., A. Wagner, and R. Zamar, Parallel Computation of high dimensional robust correlation and covariance matrices, algorithmica, 45(3), 2006 pp. 403 - 431.
 R. Cleroux, Multivariate Association and Inference Problems in Data Analysis, proceedings of the fifth international symposium on data analysis and informatics, vol. 1, Versailles, France. 1987.
 Jr, N. Da costa,. S. Nunes, P.Ceretta and S. Da Silva, Stock market comovements revisited, Economics Bulletin, 7(3), 2005, pp. 1-9.
 M. A. Djauhari, Improved Monitoring of Multivariate Variability, Journal of Quality Technology, 37(1), 2005, pp. 32-39.
 M. A. Djauhari, A Measure of Data Concentration, Journal of Probability and Statistics, 2(2), 2007, pp. 139-155.
 M. A. Djauhari, M. Mashuri, and D. E. Herwindiati, Multivariate Process Variability Monitoring, Communications in statistics - Theory and Methods, 37(1), 2008, pp. 1742 - 1754.
 H. El Maache, and Y. Lepage, Measures d-Association Vectorielle Basées sur une Matrice de Corrélation. Revue de Statistique Appliquée, 46(4), 1998, pp. 27-43.
 Y. Escoufier, Le traitement des variables vectorielles. Biometrics, 29, 1973, pp.751-760.
 A. K. Gupta, and J. Tang, Distribution of likelihood ratio statistic for testing equality of covariance matrices of multivariate Gaussian models, Biometrika, 71(3), 1984, pp. 555-559.
 D. E., Herwindiati, M. A., Djauhari, and M., Mashuri, Robust Multivariate Outlier Labeling, Communications in statistics - Computation and Simulation, 36(6), 2007, pp. 1287 - 1294.
 M., Hubert, P.J., Rouddeeuw, and S. van Aelst, Multivariate outlier detection and robustness, in handbook of statistics, vol. 24, Elsevier B.V., 2005, pp. 263-302.
 M. B. C., Khoo, and S. H. Quah, Multivariate control chart for process dispersion based on individual observations. Quality Engineering, 15(4), 2003, pp. 639-643.
 M. B. C., Khoo, and S. H. Quah, Alternatives to the multivariate control chart for process dispersion. Quality Engineering, 16(3), 2004, pp. 423- 435.
 O., Ledoit and M. Wolf, Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size. The Annals of Statistics, 30(4), 2002, pp. 1081-1102.
 K.V., Mardia, J.M. Kent, Multivariate analysis, seventh printing, Academic press, London, 2000.
 D.C. Montgomery, Introduction to statistical quality control, fourth edition, John Willey & Sons, Inc., New York, 2001.
 R. J. Muirhead, Aspects of multivariate statistical theory, John Willey & Sons, Inc., New York, 1982.
 V. Ragea, Testing correlation stability during hectic financial markets, financial market and Portfolio Management, 17(3), 2003, pp. 289-308.
 P.J. Rosseeuw, Multivariate estimation with high breakdown point. In mathematical statistics and applications, B, Grossman W., Pflug G., Vincze I and Wertz, W., editors, D. Reidel Publishing Company, 1985, pp. 283-297.
 P.J., Rosseeuw, and A.M. Leroy, Robust regression and outlier detection, John Willey & Sons, Inc., New York, 1987.
 P.J., Rosseeuw, and M. Hubert, Regression Depth, Journal of the American Statistical Association, 94, 1999, pp.388-402.
 P.J., Rosseeuw, and K. van Driessen, A fast algorithm for the minimum covariance determinant estimatior, Technometrics, 41, 1999, pp. 212 - 223.
 J., Schafer, and K.,Strimmer, A Shrinkage Approach to large scale covariance matrix estimation and implications for functional genomics. Statistical Applications in genetics and molecular biology, 4, 2005, pp 1- 30.
 J. R., Schott, Matrix analysis for statistics, John Wiley & Sons, New York, 1997.
 J. R., Schott, Some tests for the equality of covariance matrices, journal of statistical planning and inference, 94, 2001, pp 25 - 36.
 G.A.F., Seber, Multivariate Observations, John Wiley & Sons, New York, 1984.
 R.J. Serfling, Approximation Theorems of mathematical statistics, John Wiley & Sons, New York, 1980.
 J.H. Sullivan, and W.H. Woodall, A Comparison of multivariate control charts for individual observations, Journal of Quality Technology, 28(4), 1996, pp 398-408.
 J.H., Sullivan, Z.G., Stoumbos, R.L. Mason, and J.C. Young, Step down analysis for changes in the covariance matrix and other parameters, Journal of Quality Technology, 39(1), 2007, pp 66-84.
 G.Y.N. Tang, The Intertemporal stability of the covariance and correlation matrices of Hongkong Stock Returns, Applied financial economics, 8, 1998, pp 359-365.
 M. Werner, Identification of multivariate outliers in large data sets, PhD dissertation, University of Colorado at Denver, 2003
 S.J., Wierda, Multivariate statistical process control, Recent results and directions for future research, statistica neerlandica, 48(2), 1994 pp. 147- 168.
 W.H. Woodall, and D.C. Montgomery, (1999). Research issues and ideas in statistical process control, Journal of Quality Technology, 31(4), 1999, pp 376-386.