Obtaining the exact and near-exact distributions of the likelihood ratio statistic to test circular symmetry through the use of characteristic functions

2013 ◽  
Vol 28 (5) ◽  
pp. 2091-2115 ◽  
Author(s):  
Filipe J. Marques ◽  
Carlos A. Coelho
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Statistic ◽  
Characteristic Functions ◽  
Circular Symmetry ◽  
Exact Distributions

The Exact and Near-Exact Distributions of the Likelihood Ratio Statistic for the Block Sphericity Test

2010 ◽  
Author(s):  
Filipe J. Marques ◽  
Carlos A. Coelho ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Statistic ◽  
Sphericity Test ◽  
Exact Distributions

scholarly journals On the Correction of the Asymptotic Distribution of the Likelihood Ratio Statistic If Nuisance Parameters Are Estimated Based on an External Source

2014 ◽  
Vol 10 (2) ◽  
Author(s):  
Marianne Jonker ◽  
Aad Van der Vaart
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Confidence Intervals ◽  
Likelihood Ratio ◽  
Statistical Models ◽  
Likelihood Ratio Statistic ◽  
External Source ◽  
Nuisance Parameters ◽  
Testing Hypotheses

AbstractIn practice, nuisance parameters in statistical models are often replaced by estimates based on an external source, for instance if estimates were published before or a second dataset is available. Next these estimates are assumed to be known when the parameter of interest is estimated, a hypothesis is tested or confidence intervals are constructed. By this assumption, the level of the test is, in general, higher than supposed and the coverage of the confidence interval is too low. In this article, we derive the asymptotic distribution of the likelihood ratio statistic if the nuisance parameters are estimated based on a dataset that is independent of the data used for estimating the parameter of interest. This distribution can be used for correctly testing hypotheses and constructing confidence intervals. Four theoretical and practical examples are given as illustration.

Sign in / Sign up

Export Citation Format

Share Document