The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family

1994 ◽  
Vol 46 (2) ◽  
pp. 373-388 ◽  
Author(s):  
Dankmar Böhning ◽  
Ekkehart Dietz ◽  
Rainer Schaub ◽  
Peter Schlattmann ◽  
Bruce G. Lindsay
Keyword(s):  
Likelihood Ratio ◽  
Exponential Family ◽  
The One

scholarly journals On sequential versions of the generalized likelihood ratio test

1979 ◽  
Vol 86 (1) ◽  
pp. 85-90 ◽  
Author(s):  
Andrew D. Barbour
Keyword(s):  
Likelihood Ratio ◽  
Null Hypothesis ◽  
Exponential Family ◽  
Likelihood Ratio Statistic ◽  
Generalized Likelihood Ratio Test ◽  
Ratio Test ◽  
Uhlenbeck Process ◽  
Large Sample ◽  
Sequential Tests ◽  
Composite Hypotheses

AbstractIt is shown that the Wilks large sample likelihood ratio statistic λn, for testing between composite hypotheses Θ0 ⊂ Θ1 on the basis of a sample of size n, behaves as n varies like a diffusion process related to an equilibrium Ornstein-Uhlenbeck process, whenever the null hypothesis is true. This fact is used to construct large sample sequential tests based on λn, which are the same whatever the underlying distributions. In particular, the underlying distributions need not belong to an exponential family.

scholarly journals Specification of deformation congruence models using combinatorial iterative DIA testing procedure

2020 ◽  
Vol 94 (12) ◽  
Author(s):  
Krzysztof Nowel
Keyword(s):  
Likelihood Ratio ◽  
Computer Simulations ◽  
Testing Procedure ◽  
Likelihood Ratio Tests ◽  
The Other ◽  
Deformation Analysis ◽  
Characteristic Points ◽  
The One ◽  
Congruence Test ◽  
Combinatorial Methods

AbstractDeformation congruence models form the basis for conventional deformation analysis (CDA). In geometrical sense, these models connect an epochal object states—represented by its characteristic points—at stable/congruent points to disclose possible deformations. To this day, the deformation congruence models are usually specified using the global congruence test (GCT) procedure which, however, has a weakness in the case of multiple displacements. More precisely, the GCT procedure is based on consecutive point-by-point specification which may suffer from so-called displacement smearing. To overcome the above weakness, a revolutionary—in the context of GCT—concept (two methods) involving combinatorial possibilities was suggested in recent years. Admittedly, this concept avoids the problem of consecutive point-by-point specification. Nevertheless, it generates another weakness, namely the problem of the comparison of different-dimensional models. This paper makes a step forward in this new combinatorial field and discusses a more sophisticated combinatorial procedure, denoted as CIDIA. It was shown that, thanks to an appropriately used the possibilities of combinatorics and generalized likelihood ratio tests performed in the detection–identification–adaptation (DIA) iterative steps, the above weaknesses can be overcome. In the context of GCT, the suggested procedure has rather evolutionary—than revolutionary—character and the general concepts of both procedures have similar heuristic substantiation. To demonstrate the efficacy of CIDIA against GCT and the two existing combinatorial methods, various deformation scenarios were being randomized independently many times with the use of comprehensive computer simulations and then processed. Generally, the obtained results confirmed the statement that the suggested CIDIA procedure—unlike the existing combinatorial methods—can be substantially more resistant to displacement smearing than the GCT procedure, at no significant costs. The efficacy of CIDIA—unlike the ones of the two existing combinatorial methods—turned out always higher (on average by several percentages) than the one of GCT for all considered deformation scenarios. At the same time, the CIDIA procedure turned out substantially less time-consuming than the other combinatorial methods.

Glaser’s function and stochastic orders for mixture distributions

2016 ◽  
Vol 33 (8) ◽  
pp. 1230-1238
Author(s):  
Jalil Jarrahiferiz ◽  
G.R. Mohtashami Borzadaran ◽  
A.H. Rezaei Roknabadi
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Exponential Family ◽  
Random Variable ◽  
Moment Generating Function ◽  
Stochastic Orders ◽  
Weight Functions ◽  
Likelihood Ratio Order ◽  
Content Type ◽  
Weighted Distributions

Purpose The purpose of this paper is to study likelihood ratio order for mixture and its components via their Glaser’s functions for weighted distributions. So, some theoretical examples using exponential family and their mixtures are presented. Design/methodology/approach First, Glaser’s functions of mixture and its components for weighted distributions in different scenarios are computed. Then by them the likelihood ratio order is investigated between mixture and its components. Findings The authors find conditions for weight functions under which the mixture random variable is between of its components in likelihood ratio order. Originality/value Results are obtained for weight function in general. It is well known that the some special weights are order statistics, up and down records, hazard rate, reversed hazard rate, moment generating function, etc. So, the results are valid for all of them.

scholarly journals A Class of Nonlinear Admissible Estimators in the One-Parameter Exponential Family

1981 ◽  
Vol 9 (1) ◽  
pp. 177-183 ◽  
Author(s):  
Dan Ralescu ◽  
Stefan Ralescu
Keyword(s):  
Exponential Family ◽  
The One
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