A notion of an obstructive residual likelihood

1987 ◽  
Vol 39 (2) ◽  
pp. 247-261 ◽  
Author(s):  
Takemi Yanagimoto
Keyword(s):  
Residual Likelihood

Factorizations of the residual likelihood criterion in discriminant analysis

1966 ◽  
Vol 62 (4) ◽  
pp. 743-752 ◽  
Author(s):  
J. Radcliffe
Keyword(s):  
Discriminant Analysis ◽  
Confidence Intervals ◽  
Goodness Of Fit ◽  
Discriminant Functions ◽  
Approximate Factorization ◽  
Analytic Proof ◽  
Independent Variables ◽  
Canonical Variables ◽  
Residual Likelihood ◽  
The Difference

Certain exact tests were developed by Williams (1952) to deal with the goodness of fit of a single hypothetical discriminant function. Bartlett (1951) generalized these results by the use of the geometric method to any number of dependent and independent variables. Bartlett's paper is divided into two parts. The first deals with an approximate factorization of the residual likelihood criterion into an effect due to the difference between the hypothetical and sample functions, and an effect due to non-collinearity. A method is given for constructing confidence intervals from the first factor. The second part of the paper gives two possible exact factorizations of the likelihood criterion, expressing the results in terms of the sample canonical variables. Kshirsagar (1964a) has expressed these results in terms of the original variables and given an analytic proof of the distribution of the factors. Williams (1955, 1961) has outlined a generalization of these results to several discriminant functions and given the result for one of the possible factorizations.

The distributions of certain factors occurring in discriminant analysis

1968 ◽  
Vol 64 (3) ◽  
pp. 731-740 ◽  
Author(s):  
J. Radcliffe
Keyword(s):  
Discriminant Analysis ◽  
Discriminant Function ◽  
Sample Space ◽  
Matrix Transformations ◽  
Discriminant Functions ◽  
Significance Tests ◽  
Test Criteria ◽  
Residual Likelihood

AbstractSignificance tests for several hypothetical discriminant functions have been developed by Williams (7,8) and considered further by the author (6). The test criteria consist of the factors in certain factorizations of the residual likelihood criterion, when the effect of the hypothetical discriminant functions has been eliminated. The independence and distributions of the factors can be seen by geometrical considerations, to be a consequence of the manner in which the factors are constructed in the sample space. In the case of a single hypothetical discriminant function Kshirsagar (5) has produced analytic proofs, by means of matrix transformations, of the independence and distributions of the factors. In this paper we shall give analytic proofs of the independence and distributions of the factors, given in sections 4 and 5 of the authors' paper (6), by extending Kshirsagar's proof to the case of several hypothetical discriminant functions.

scholarly journals Criteria for longitudinal data model selection based on Kullback’s symmetric divergence

2012 ◽  
Vol Volume 15, 2012 ◽  
Author(s):  
Bezza Hafidi ◽  
Nourddine Azzaoui
Keyword(s):  
Model Selection ◽  
Longitudinal Data ◽  
Data Model ◽  
Small Samples ◽  
Correlated Errors ◽  
Residual Likelihood ◽  
International Audience ◽  
Selection For ◽  
Aic Criterion ◽  
New Criteria

International audience Recently, Azari et al (2006) showed that (AIC) criterion and its corrected versions cannot be directly applied to model selection for longitudinal data with correlated errors. They proposed two model selection criteria, AICc and RICc, by applying likelihood and residual likelihood approaches. These two criteria are estimators of the Kullback-Leibler's divergence distance which is asymmetric. In this work, we apply the likelihood and residual likelihood approaches to propose two new criteria, suitable for small samples longitudinal data, based on the Kullback's symmetric divergence. Their performance relative to others criteria is examined in a large simulation study

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