Title

t-distribution modeling using the available statistical software

Authors

Authors

M. Jamshidian

Comments

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Abbreviated Journal Title

Comput. Stat. Data Anal.

Keywords

BMDP-LE; linear regression; nonlinear regression; normal/independent; distribution; robust estimation; SAS-NLIN; EM; Computer Science, Interdisciplinary Applications; Statistics &; Probability

Abstract

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.

Journal Title

Computational Statistics & Data Analysis

Volume

25

Issue/Number

2

Publication Date

1-1-1997

Document Type

Article

Language

English

First Page

181

Last Page

206

WOS Identifier

WOS:A1997XN78300005

ISSN

0167-9473

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