Degeneracy in Heteroscedastic Regression Models

• Published in: Journal of multivariate analysis Vol. 74; no. 2; pp. 282 - 295
• Main Authors: Li, Kim-Hung, Chan, Nai Ng
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.08.2000; Elsevier
• Series: Journal of Multivariate Analysis
• Subjects: degeneracy; degeneracy, generalized linear model with varying dispersion, heteroscedastic error, unbounded likelihood; Exact sciences and technology; generalized linear model with varying dispersion; heteroscedastic error; Linear inference, regression; Mathematics; Parametric inference; Probability and statistics; Sciences and techniques of general use; Statistics; unbounded likelihood; degeneracy, generalized linear model with varying dispersion, heteroscedastic error, unbounded likelihood; Necessary condition; Maximum likelihood; Regression model; Degenerate system; Linear model; Heteroscedasticity
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1006/jmva.1999.1887

The maximum likelihood estimation in a regression model with heteroscedastic errors is considered. When the design matrices in the model are inappropriately specified, the maximum likelihood estimates of the variances of certain observations are found to be zero irrespective of the observed values, resulting in degeneracy. Necessary and sufficient conditions for degeneracy are given and used for its avoidance.