Likelihood ratio tests with boundary constraints using data-dependent degrees of freedom

Biometrika ◽  
2013 ◽  
Vol 100 (4) ◽  
pp. 1019-1023 ◽  
Author(s):  
E. Susko
Keyword(s):  
Likelihood Ratio ◽  
Degrees Of Freedom ◽  
Likelihood Ratio Tests ◽  
Boundary Constraints ◽  
Using Data

scholarly journals ADMISSIBLE INVARIANT SIMILAR TESTS FOR INSTRUMENTAL VARIABLES REGRESSION

2009 ◽  
Vol 25 (3) ◽  
pp. 806-818 ◽  
Author(s):  
Victor Chernozhukov ◽  
Christian Hansen ◽  
Michael Jansson
Keyword(s):  
Likelihood Ratio ◽  
Instrumental Variables ◽  
Degrees Of Freedom ◽  
Average Power ◽  
Weighted Average ◽  
Likelihood Ratio Tests ◽  
Weak Instruments ◽  
Working Paper ◽  
Statistical Sense ◽  
Limiting Case

This paper studies a model widely used in the weak instruments literature and establishes admissibility of the weighted average power likelihood ratio tests recently derived by Andrews, Moreira, and Stock (2004, NBER Technical Working Paper 199). The class of tests covered by this admissibility result contains the Anderson and Rubin (1949, Annals of Mathematical Statistics 20, 46–63) test. Thus, there is no conventional statistical sense in which the Anderson and Rubin (1949) test “wastes degrees of freedom.” In addition, it is shown that the test proposed by Moreira (2003, Econometrica 71, 1027–1048) belongs to the closure of (i.e., can be interpreted as a limiting case of) the class of tests covered by our admissibility result.

A Note on the Asymptotic Distribution of Likelihood Ratio Tests to Test Variance Components

2006 ◽  
Vol 9 (4) ◽  
pp. 490-495 ◽  
Author(s):  
Peter M. Visscher
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Distribution ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Variance Components ◽  
Degrees Of Freedom ◽  
Likelihood Ratio Tests ◽  
Likelihood Ratio Test Statistic ◽  
Ratio Test ◽  
Test Statistic

AbstractWhen using maximum likelihood methods to estimate genetic and environmental components of (co)variance, it is common to test hypotheses using likelihood ratio tests, since such tests have desirable asymptotic properties. In particular, the standard likelihood ratio test statistic is assumed asymptotically to follow a χ2 distribution with degrees of freedom equal to the number of parameters tested. Using the relationship between least squares and maximum likelihood estimators for balanced designs, it is shown why the asymptotic distribution of the likelihood ratio test for variance components does not follow a χ2 distribution with degrees of freedom equal to the number of parameters tested when the null hypothesis is true. Instead, the distribution of the likelihood ratio test is a mixture of χ2 distributions with different degrees of freedom. Implications for testing variance components in twin designs and for quantitative trait loci mapping are discussed. The appropriate distribution of the likelihood ratio test statistic should be used in hypothesis testing and model selection.

scholarly journals Quasi-likelihood ratio tests for cointegration, cobreaking, and cotrending

2019 ◽  
Vol 38 (8) ◽  
pp. 881-898
Author(s):  
Josep Lluís Carrion-i-Silvestre ◽  
Dukpa Kim
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Tests
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