ERROR DETECTION IN GENETIC LINKAGE DATA FOR HUMAN PEDIGREES USING LIKELIHOOD RATIO METHODS

1995 ◽  
Vol 03 (01) ◽  
pp. 13-25 ◽  
Author(s):  
MARGARET GELDER EHM ◽  
MAREK KIMMEL ◽  
ROBERT W. COTTINGHAM
Keyword(s):  
Likelihood Ratio ◽  
Error Detection ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Recombination Fraction ◽  
Linkage Data ◽  
Ratio Test ◽  
Pedigree Data ◽  
Test Statistic ◽  
Typing Error

The occurrence of laboratory typing error in pedigree data collected for use in linkage analysis cannot be ignored. In maps where recombinations between nearby markers rarely occur, each erroneous recombinations (result of typing error) is given substantial weight thereby increasing the estimate of θ, the recombination fraction. As the maps being developed become more dense, θ approaches the error rate and most of all observed crossovers will be erroneous. We present a method for detecting errors in pedigree data. The index is a variant of the likelihood ratio test statistic and is used to test the null hypothesis of no error for an individual at a locus versus the alternative hypothesis of error. High values of the index correspond to unlikely genotypes. The method has been shown to detect errors introduced into CEPH pedigrees and an error in a larger experimental pedigree (retinitis pigmentosa). While the method was designed to detect typing error, it is sufficiently general to detect any relatively unlikely genotype and therefore can also be used to detect pedigree error.

Improved Tests for an Ordered Hypothesis in one Parameter Exponential Families

1993 ◽  
Vol 43 (1-2) ◽  
pp. 57-64
Author(s):  
Teng Li
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Subject Classification ◽  
Exponential Families ◽  
Ratio Test ◽  
Primary 62F03 ◽  
Special Cases

We consider m independent one parameter exponential families with parameters (θ1, θ2,  , θ m), and the alternative hypothesis [Formula: see text] where [Formula: see text] are specified. The null hypothesis Ho is the complement of H1. A class of tests more powerful than the likelihood ratio test (LRT) is derived. Applications to two special cases, Binomial and Poisson, are indicated. AMS 1980 Subject Classification: Primary 62F03

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 Monitoring Persistence Change in Heavy-Tailed Observations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 936
Author(s):  
Dan Wang
Keyword(s):  
Kernel Method ◽  
Alternative Hypothesis ◽  
Null Distribution ◽  
Real Data ◽  
Ratio Test ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Approximation ◽  
Heavy Tailed ◽  
Better Than

In this paper, a ratio test based on bootstrap approximation is proposed to detect the persistence change in heavy-tailed observations. This paper focuses on the symmetry testing problems of I(1)-to-I(0) and I(0)-to-I(1). On the basis of residual CUSUM, the test statistic is constructed in a ratio form. I prove the null distribution of the test statistic. The consistency under alternative hypothesis is also discussed. However, the null distribution of the test statistic contains an unknown tail index. To address this challenge, I present a bootstrap approximation method for determining the rejection region of this test. Simulation studies of artificial data are conducted to assess the finite sample performance, which shows that our method is better than the kernel method in all listed cases. The analysis of real data also demonstrates the excellent performance of this method.

scholarly journals On sequential versions of the generalized likelihood ratio test

1979 ◽  
Vol 86 (1) ◽  
pp. 85-90 ◽  
Author(s):  
Andrew D. Barbour
Keyword(s):  
Likelihood Ratio ◽  
Null Hypothesis ◽  
Exponential Family ◽  
Likelihood Ratio Statistic ◽  
Generalized Likelihood Ratio Test ◽  
Ratio Test ◽  
Uhlenbeck Process ◽  
Large Sample ◽  
Sequential Tests ◽  
Composite Hypotheses

AbstractIt is shown that the Wilks large sample likelihood ratio statistic λn, for testing between composite hypotheses Θ0 ⊂ Θ1 on the basis of a sample of size n, behaves as n varies like a diffusion process related to an equilibrium Ornstein-Uhlenbeck process, whenever the null hypothesis is true. This fact is used to construct large sample sequential tests based on λn, which are the same whatever the underlying distributions. In particular, the underlying distributions need not belong to an exponential family.

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