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MOMENTS OF VARIOGRAM ESTIMATOR FOR A GENERALIZED SKEW t DISTRIBUTION  

KIM HYOUNG-MOON (Department of Applied Statistics, Konkuk University)
Publication Information
Journal of the Korean Statistical Society / v.34, no.2, 2005 , pp. 109-123 More about this Journal
Abstract
Variogram estimation is an important step of spatial statistics since it determines the kriging weights. Matheron's variogram estimator can be written as a quadratic form of the observed data. In this paper, we extend a skew t distribution to a generalized skew t distribution and moments of the variogram estimator for a generalized skew t distribution are derived in closed forms. After calculating the correlation structure of the variogram estimator, variogram fitting by generalized least squares is discussed.
Keywords
Multivariate generalized skew t distribution; quadratic form; skewness; kurtosis; generalized least squares;
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1 GORSICH, D.J., GENTON, M.G., AND STRANG, G. (2002). 'Eigenstructures of Spatial Design Matrices', Journal of Multivariate Analysis, 80, 138-165   DOI   ScienceOn
2 KIM, H.-M., MALLICK, B.K. (2003). 'Moments of random vectors with skew t distribution and their quadratic forms', Statistics & Probability Letters, 63, 417-423   DOI   ScienceOn
3 SCHOTT, JAMES R. (1997). Matrix Analysis for Statistics, Wiley, New York
4 ARELLANO-VALLE, R.B. AND BOLFARINE, H. (1995). 'On some characterizations of the t-distribution', Statistics & Probability Letters, 25, 79-85   DOI   ScienceOn
5 AZZALINI, A. AND DALLA VALLE, A. (1996). 'The multivariate skew-normal distribution', Biometrika, 83, 715-726   DOI   ScienceOn
6 MUIRHEAD, R.J. (1982). Aspects of Multivariate Statistical Theory, WHey, New York
7 GENTON, M.G. (1998b). 'Highly robust Variogram estimation', Mathematical Geology, 30, 213-221   DOI   ScienceOn
8 GENTON, M.G. (2000). 'The correlation structure of Matheron's classical variogram estimator under elliptically contoured distributions', Mathematical Geology, 32, 127-137   DOI   ScienceOn
9 MARDIA, K.V. (1970). 'Measures of multivariate skewness and kurtosis with applications', Biometrika, 57, 519-530   DOI   ScienceOn
10 AZZALINI, A. AND CAPITANIO (1999). 'Statistical applications of the multivariate skew normal distribution', Journal of the Royal Statistical Society Series B, 61, 579-602   DOI   ScienceOn
11 FANG, K.-T., KOTZ, S., AND NG, K.W. (1989). Symmetric Multivariate and Related Distributions, Chapman and Hall, New York
12 LI, G. (1987). 'Moments of a random vector and its quadratic forms', Journal of Statistical Applied Probability, 2, 219-229
13 CRESSIE, N. (1993). Statistics for Spatial Data (rev. ed.), WHey, New York
14 GENTON, M.G. (1998a). 'Variogram fitting by generalized least squares using an explicit formula for the covariance structure', Mathematical Geology, 30, 323-345   DOI   ScienceOn
15 AZZALINI, A. AND CAPITANIO (2003). 'Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution', Journal of the Royal Statistical Society Series B, 65, 367-389   DOI   ScienceOn
16 HENDERSON, H.V. AND SEARLE, S.R. (1981). 'On deriving the inverse of a sum of matrices', SIAM Review, 33, 53-60   DOI   ScienceOn
17 GENTON, M.G., HE, L. AND LIU, X. (2001). 'Moments of skew-normal random vectors and their quadratic forms', Statistics & Probability Letters, 51, 319-325   DOI   ScienceOn
18 MARDIA, K.V. (1974). 'Applications of some measures of multivariate skewness and kurtosis in testing normality and robustness studies', Sankhya Ser. B, 36, 115-128