On existence and uniqueness of maximum likelihood estimates in quantal and ordinal response models

Metrika ◽  
1988 ◽  
Vol 35 (1) ◽  
pp. 291-313 ◽  
Author(s):  
H. Kaufmann
Keyword(s):  
Maximum Likelihood ◽  
Existence And Uniqueness ◽  
Maximum Likelihood Estimates ◽  
Response Models ◽  
Ordinal Response

EXISTENCE AND UNIQUENESS OF CHAIN LADDER SOLUTIONS

2016 ◽  
Vol 47 (1) ◽  
pp. 1-41 ◽  
Author(s):  
Greg Taylor
Keyword(s):  
Maximum Likelihood ◽  
Existence And Uniqueness ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
The Cross ◽  
Chain Ladder ◽  
Ladder Models

AbstractThe cross-classified chain ladder has a number of versions, depending on the distribution to which observations are subject. The simplest case is that of Poisson distributed observations, and then maximum likelihood estimates of parameters are explicit. Most other cases, however, including Bayesian chain ladder models, lead to implicit MAP (Bayesian) or MLE (non-Bayesian) solutions for these parameter estimates, raising questions as to their existence and uniqueness. The present paper investigates these questions in the case where observations are distributed according to some member of the exponential dispersion family.

scholarly journals Directional Selection and the Site-Frequency Spectrum

Genetics ◽  
2001 ◽  
Vol 159 (4) ◽  
pp. 1779-1788 ◽  
Author(s):  
Carlos D Bustamante ◽  
John Wakeley ◽  
Stanley Sawyer ◽  
Daniel L Hartl
Keyword(s):  
Maximum Likelihood ◽  
High Power ◽  
Negative Selection ◽  
Likelihood Estimation ◽  
Directional Selection ◽  
Likelihood Ratio Tests ◽  
Maximum Likelihood Estimates ◽  
Likelihood Methods ◽  
Ancestral States ◽  
Asymptotic Variances

Abstract In this article we explore statistical properties of the maximum-likelihood estimates (MLEs) of the selection and mutation parameters in a Poisson random field population genetics model of directional selection at DNA sites. We derive the asymptotic variances and covariance of the MLEs and explore the power of the likelihood ratio tests (LRT) of neutrality for varying levels of mutation and selection as well as the robustness of the LRT to deviations from the assumption of free recombination among sites. We also discuss the coverage of confidence intervals on the basis of two standard-likelihood methods. We find that the LRT has high power to detect deviations from neutrality and that the maximum-likelihood estimation performs very well when the ancestral states of all mutations in the sample are known. When the ancestral states are not known, the test has high power to detect deviations from neutrality for negative selection but not for positive selection. We also find that the LRT is not robust to deviations from the assumption of independence among sites.

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