Likelihood inference in exponential families and directions of recession
TL;DR: In this article, the authors propose an algorithm for finding the maximum likelihood estimate (MLE) in the Barndor-Nielsen completion of the full exponential family, where the MLE of the natural parameter can be thought of as having gone to infinity in a certain direction, which they call a generic di- rection of recession.
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Abstract: When in a full exponential family the maximum likelihood es- timate (MLE) does not exist, the MLE may exist in the Barndor-Nielsen completion of the family. We propose a practical algorithm for finding the MLE in the completion based on repeated linear programming using the R contributed package rcdd and illustrate it with two generalized linear model examples. When the MLE for the null hypothesis lies in the comple- tion, likelihood ratio tests of model comparison are almost unchanged from the usual case. Only the degrees of freedom need to be adjusted. When the MLE lies in the completion, confidence intervals are changed much more from the usual case. The MLE of the natural parameter can be thought of as having gone to infinity in a certain direction, which we call a generic di- rection of recession. We propose a new one-sided confidence interval which says how close to infinity the natural parameter may be. This maps to one-sided confidence intervals for mean values showing how close to the boundary of their support they may be.
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On the geometry of discrete exponential families with application to exponential random graph models
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•Posted Content
On the Geometry of Discrete Exponential Families with Application to Exponential Random Graph Models
TL;DR: It is shown that the normal fan of P is a geometric object that plays a fundamental role in deriving the statis- tical and geometric properties of the corresponding extended exponential families of distribution with discrete base measure and polyhedral convex support P.
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References
•Book
The Elements of Statistical Learning
Trevor Hastie,Robert Tibshirani,Jerome H. Friedman +2 more
- 01 Jan 2001
29.4K
The elements of statistical learning. 2001
Trevor Hastie,Robert Tibshirani,Jerome H. Friedman +2 more
- 01 Jan 2001
17.2K
The Elements of Statistical Learning
TL;DR: Chapter 11 includes more case studies in other areas, ranging from manufacturing to marketing research, and a detailed comparison with other diagnostic tools, such as logistic regression and tree-based methods.
15.5K
Categorical Data Analysis
TL;DR: In this article, categorical data analysis was used for categorical classification of categorical categorical datasets.Categorical Data Analysis, categorical Data analysis, CDA, CPDA, CDSA
15.1K