Title

t-distribution modeling using the available statistical software

Keywords

BMDP-LE; Linear regression; Nonlinear regression; Normal/independent distribution; Robust estimation; SAS-NLIN

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. © 1997 Elsevier Science B.V.

Publication Date

7-31-1997

Publication Title

Computational Statistics and Data Analysis

Volume

25

Issue

2

Number of Pages

181-206

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/S0167-9473(96)00091-6

Socpus ID

0031182503 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0031182503

This document is currently not available here.

Share

COinS