We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Semiparametric Mixtures of Generalized Exponential Families.
- Authors
Charnigo, Richard; Pilla, Ramani S.
- Abstract
A semiparametric mixture model is characterized by a non-parametric mixing distribution (with respect to a parameter θ) and a structural parameter β common to all components. Much of the literature on mixture models has focused on fixing β and estimating . However, this can lead to inconsistent estimation of both and the order of the model m. Creating a framework for consistent estimation remains an open problem and is the focus of this article. We formulate a class of generalized exponential family (GEF) models and establish sufficient conditions for the identifiability of finite mixtures formed from a GEF along with sufficient conditions for a nesting structure. Finite identifiability and nesting structure lead to the central result that semiparametric maximum likelihood estimation of and β fails. However, consistent estimation is possible if we restrict the class of mixing distributions and employ an information-theoretic approach. This article provides a foundation for inference in semiparametric mixture models, in which GEFs and their structural properties play an instrumental role.
- Subjects
EXPONENTIAL families (Statistics); DISTRIBUTION (Probability theory); LAPLACE transformation; DIFFERENTIAL equations; OPERATIONAL calculus; MATHEMATICAL transformations; GENERALIZED estimating equations; MIXTURE distributions (Probability theory); GAUSSIAN distribution; LINEAR statistical models
- Publication
Scandinavian Journal of Statistics, 2007, Vol 34, Issue 3, p535
- ISSN
0303-6898
- Publication type
Article
- DOI
10.1111/j.1467-9469.2006.00532.x