scholarly journals Likelihood Ratio Test in Multivariate Linear Regression: from Low to High Dimension

2021 ◽  
Author(s):  
Yinqiu He ◽  
Tiefeng Jiang ◽  
Jiyang Wen ◽  
Gongjun Xu
Keyword(s):  
Linear Regression ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
High Dimension ◽  
Multivariate Linear Regression ◽  
Ratio Test

scholarly journals Likelihood Ratio Test in the Two Phase Linear Regression Problem.

1997 ◽  
Vol 26 (3) ◽  
pp. 135-150 ◽  
Author(s):  
Qi BIAN ◽  
Wataru SAKAMOTO ◽  
Shingo SHIRAHATA
Keyword(s):  
Linear Regression ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Ratio Test ◽  
Two Phase ◽  
Regression Problem ◽  
Linear Regression Problem

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 Scan Statistics for Detecting High-Variance Clusters

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Lionel Cucala
Keyword(s):  
Linear Regression ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
High Variability ◽  
Scan Statistics ◽  
Generalized Likelihood Ratio Test ◽  
Ratio Test ◽  
Time Intervals ◽  
New Methods ◽  
The Mean

Scan statistics are mostly used to detect spatial areas or time intervals in which the mean level of a given variable is more important. Sometimes, when this variable is continuous, there is an interest in looking for clusters in which its variability is more important. In this paper, two scan statistics are introduced for identifying clusters of values exhibiting higher variance. Like many classical scan statistics, the first one relies on a generalized likelihood ratio test whereas the second one is based on ratios of empirical variances. These methods are useful to identify spatial areas or time intervals in which the variability of a given variable is more important. In an application of the new methods, I look for geographical clusters of high-variability income in France and then for residuals exhibiting higher variance in a linear regression context.

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