Building a Confidence Interval for the Number of Signals in Noise using Likelihood Ratio Test Statistics

2006 ◽  
Author(s):  
J.S. Markow ◽  
M.C. Wicks ◽  
Pinyuen Chen
Keyword(s):  
Confidence Interval ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Ratio Test ◽  
Test Statistics

scholarly journals On the use of linear regression and maximum likelihood for QTL mapping in half-sib designs

1998 ◽  
Vol 72 (2) ◽  
pp. 149-158 ◽  
Author(s):  
P. V. BARET ◽  
S. A. KNOTT ◽  
P. M. VISSCHER
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Ratio Test ◽  
Test Statistics ◽  
Daughter Design ◽  
Practical Implications

Methods of identification of quantitative trait loci (QTL) using a half-sib design are generally based on least-squares or maximum likelihood approaches. These methods differ in the genetical model considered and in the information used. Despite these differences, the power of the two methods in a daughter design is very similar. Using an analogy with a one-way analysis of variance, we propose an equation connecting the two test-statistics (F ratio for regression and likelihood ratio test in the case of the maximum likelihood). The robustness of this relationship is tested by simulation for different single QTL models. In general, the correspondence between the two statistics is good under both the null hypothesis and the alternative hypothesis of a single QTL segregating. Practical implications are discussed with particular emphasis on the theoretical distribution of the likelihood ratio test.

scholarly journals Bartlett-corrected tests for varying precision beta regressions with application to environmental biometrics

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0253349
Author(s):  
Ana C. Guedes ◽  
Francisco Cribari-Neto ◽  
Patrícia L. Espinheira
Keyword(s):  
Sample Size ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Superior Performance ◽  
Model Parameters ◽  
Ratio Test ◽  
Test Statistics ◽  
Finite Sample ◽  
Alternative Approach ◽  
The Mean

Beta regressions are commonly used with responses that assume values in the standard unit interval, such as rates, proportions and concentration indices. Hypothesis testing inferences on the model parameters are typically performed using the likelihood ratio test. It delivers accurate inferences when the sample size is large, but can otherwise lead to unreliable conclusions. It is thus important to develop alternative tests with superior finite sample behavior. We derive the Bartlett correction to the likelihood ratio test under the more general formulation of the beta regression model, i.e. under varying precision. The model contains two submodels, one for the mean response and a separate one for the precision parameter. Our interest lies in performing testing inferences on the parameters that index both submodels. We use three Bartlett-corrected likelihood ratio test statistics that are expected to yield superior performance when the sample size is small. We present Monte Carlo simulation evidence on the finite sample behavior of the Bartlett-corrected tests relative to the standard likelihood ratio test and to two improved tests that are based on an alternative approach. The numerical evidence shows that one of the Bartlett-corrected typically delivers accurate inferences even when the sample is quite small. An empirical application related to behavioral biometrics is presented and discussed.

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