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 GENERALIZED AUTOREGRESSIVE CONDITIONAL CORRELATION

2008 ◽  
Vol 24 (6) ◽  
pp. 1554-1583 ◽  
Author(s):  
Michael McAleer ◽  
Felix Chan ◽  
Suhejla Hoti ◽  
Offer Lieberman
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Autoregressive Process ◽  
American Statistical Association ◽  
Random Coefficient ◽  
Regularity Conditions ◽  
Ratio Test ◽  
Conditional Correlation ◽  
Economic Statistics ◽  
Special Cases

This paper develops a generalized autoregressive conditional correlation (GARCC) model when the standardized residuals follow a random coefficient vector autoregressive process. As a multivariate generalization of the Tsay (1987, Journal of the American Statistical Association 82, 590–604) random coefficient autoregressive (RCA) model, the GARCC model provides a motivation for the conditional correlations to be time varying. GARCC is also more general than the Engle (2002, Journal of Business & Economic Statistics 20, 339–350) dynamic conditional correlation (DCC) and the Tse and Tsui (2002, Journal of Business & Economic Statistics 20, 351–362) varying conditional correlation (VCC) models and does not impose unduly restrictive conditions on the parameters of the DCC model. The structural properties of the GARCC model, specifically, the analytical forms of the regularity conditions, are derived, and the asymptotic theory is established. The Baba, Engle, Kraft, and Kroner (BEKK) model of Engle and Kroner (1995, Econometric Theory 11, 122–150) is demonstrated to be a special case of a multivariate RCA process. A likelihood ratio test is proposed for several special cases of GARCC. The empirical usefulness of GARCC and the practicality of the likelihood ratio test are demonstrated for the daily returns of the Standard and Poor's 500, Nikkei, and Hang Seng indexes.

scholarly journals ADMISSIBLE SIGNIFICANCE TESTS IN SIMULTANEOUS EQUATION MODELS

2017 ◽  
Vol 33 (3) ◽  
pp. 534-550
Author(s):  
Theodore W. Anderson
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Structural Equation ◽  
Alternative Hypothesis ◽  
Simultaneous Equation ◽  
Reduced Form ◽  
Ratio Test ◽  
Linear Transformations ◽  
Significance Level ◽  
Endogenous Variables

Consider testing the null hypothesis that a single structural equation has specified coefficients. The alternative hypothesis is that the relevant part of the reduced form matrix has proper rank, that is, that the equation is identified. The usual linear model with normal disturbances is invariant with respect to linear transformations of the endogenous and of the exogenous variables. When the disturbance covariance matrix is known, it can be set to the identity, and the invariance of the endogenous variables is with respect to orthogonal transformations. The likelihood ratio test is invariant with respect to these transformations and is the best invariant test. Furthermore it is admissible in the class of all tests. Any other test has lower power and/or higher significance level. In particular, this likelihood ratio test dominates a test based on the Two-Stage Least Squares estimator.

scholarly journals Exact Tests of Zero Variance Component in Presence of Multiple Variance Components with Application to Longitudinal Microbiome Study

2018 ◽  
Author(s):  
Jing Zhai ◽  
Kenneth Knox ◽  
Homer L. Twigg ◽  
Hua Zhou ◽  
Jin J. Zhou
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Variance Components ◽  
Null Hypothesis ◽  
Variance Component ◽  
Ratio Test ◽  
Type I ◽  
Exact Tests ◽  
Sample Sizes ◽  
Microbiome Composition

SummaryIn the metagenomics studies, testing the association of microbiome composition and clinical conditions translates to testing the nullity of variance components. Computationally efficient score tests have been the major tools. But they can only apply to the null hypothesis with a single variance component and when sample sizes are large. Therefore, they are not applicable to longitudinal microbiome studies. In this paper, we propose exact tests (score test, likelihood ratio test, and restricted likelihood ratio test) to solve the problems of (1) testing the association of the overall microbiome composition in a longitudinal design and (2) detecting the association of one specific microbiome cluster while adjusting for the effects from related clusters. Our approach combines the exact tests for null hypothesis with a single variance component with a strategy of reducing multiple variance components to a single one. Simulation studies demonstrate that our method has correct type I error rate and superior power compared to existing methods at small sample sizes and weak signals. Finally, we apply our method to a longitudinal pulmonary microbiome study of human immunodeficiency virus (HIV) infected patients and reveal two interesting genera Prevotella and Veillonella associated with forced vital capacity. Our findings shed lights on the impact of lung microbiome to HIV complexities. The method is implemented in the open source, high-performance computing language Julia and is freely available at https://github.com/JingZhai63/VCmicrobiome.

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.

A Likelihood-Ratio Test of Twin Zygosity Using Molecular Genetic Markers

2008 ◽  
Vol 11 (1) ◽  
pp. 41-43 ◽  
Author(s):  
Stephen Erickson
Keyword(s):  
Likelihood Ratio ◽  
Genetic Markers ◽  
Likelihood Ratio Test ◽  
Twin Pair ◽  
Alternative Hypothesis ◽  
Molecular Genetic ◽  
Allele Frequencies ◽  
Ratio Test ◽  
Conditional Probabilities ◽  
Unconditional Probability

AbstractThe importance of using multiple polymorphic genetic markers to determine unambiguously whether a twin pair is monozygotic (MZ) or dizygotic (DZ) has long been recognized. Concordance among a set of markers is used as evidence of monozygosity, as it would be improbable for DZ twins to be concordant at a large number of polymorphic loci. Several sources give a formula for the probability of two DZ twins sharing the same genotype at a locus, assuming knowledge of allele frequencies but not of either twin's genotype; this probability can be used to determine whether a set of markers will reliably distinguish between MZ and DZ status in a randomly selected twin pair. If the shared genotype is known, however, the likelihood-ratio test (LRT) of the null hypothesis of dizygosity against the alternative hypothesis of monozygosity takes into account the observed genotype and, by the Neyman-Pearson lemma, is the most powerful test of its size. The LRT is equivalent to conditioning on the genotype of one of the twins, and computing the probability, assuming DZ status, of the other twin sharing that genotype. The resultingpvalues are frequently lower than those produced by the unconditional probability, especially if rare alleles are observed. The unconditional probability can be recapitulated from conditional probabilities by averaging across all of the conditioned sibling's possible genotypes. To illustrate properties of the LRT applied to multiple markers, the probability distribution of the LRTpvalue is computed from allele frequencies of twelve unlinked markers published in Elbaz et al. (2006) and compared with thepvalue computed from unconditional probabilities.

A likelihood ratio test for detecting patterns of disease-marker association

1997 ◽  
Vol 61 (4) ◽  
pp. 335-350 ◽  
Author(s):  
A. P. MORRIS ◽  
J. C. WHITTAKER ◽  
R. N. CURNOW
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Ratio Test ◽  
Disease Marker
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