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Robust Statistical Modeling Using the t Distribution

Kenneth L. Lange, Roderick J. A. Little and Jeremy M. G. Taylor
Journal of the American Statistical Association
Vol. 84, No. 408 (Dec., 1989), pp. 881-896
DOI: 10.2307/2290063
Stable URL: http://www.jstor.org/stable/2290063
Page Count: 16
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Robust Statistical Modeling Using the t Distribution
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Abstract

The t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer-than-normal tails. An analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems, including linear and nonlinear regression, robust estimation of the mean and covariance matrix with missing data, unbalanced multivariate repeated-measures data, multivariate modeling of pedigree data, and multivariate nonlinear regression. The degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference, with moderate increases in computational complexity for many models. Estimation of precision from asymptotic theory and the bootstrap is discussed, and graphical methods for checking the appropriateness of the t distribution are presented.

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