t-distribution modeling using the available statistical software
Abbreviated Journal Title
Comput. Stat. Data Anal.
BMDP-LE; linear regression; nonlinear regression; normal/independent; distribution; robust estimation; SAS-NLIN; EM; Computer Science, Interdisciplinary Applications; Statistics &; Probability
Statistical inference based on the t-distribution is less vulnerable to outliers when compared to the normal distribution. A number of authors have discussed and proposed algorithms for maximum likelihood (ML) estimation of the t-distribution. These algorithms generally require special code, to date, not available in commonly used statistical software. In this paper we discuss the use of the available statistical software for ML estimation of the t-distribution. More specifically, we discuss utilization of BMDP-LE and SAS-NLIN programs for linear and nonlinear regression with t errors. BMDP-LE program instructions require specification of the t density. The problem is that the t density involves the gamma function which is not available in the BMDP function library. We make use of the available functions in BMDP-LE to specify the t density. We show how SAS-NLIN can be used to implement a previously proposed iteratively reweighted least-squares algorithm. We also propose a direct method of using SAS-NLIN for regression estimation with t errors. The SAS-NLIN methods discussed may be implemented in any nonlinear regression program which allows iterative reweighting. The advantages and disadvantages of each method is discussed. Finally, we give a linear and a nonlinear regression example. With minor modifications, the BMDP and SAS input files given for our examples can be used to fit any linear or nonlinear regression model, assuming t distributed errors, to data. (C) 1997 Elsevier Science B.V.
Computational Statistics & Data Analysis
"t-distribution modeling using the available statistical software" (1997). Faculty Bibliography 1990s. 1952.