Likelihood-ratio test

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	Likelihood-ratio test - Wikipédia
		Many common test statistics such as the Z-test, the F-test and Uji kuadrat-chi Pearson can be phrased as log-likelihood ratios or approximations thereof.
		The likelihood-ratio test rejects the null hypothesis if the value of this statistic is too small, and is justified by the Neyman-Pearson lemma.
		For the general contingency table, we can write the log-likelihood ratio statistic as
	su.wikipedia.org /wiki/Likelihood-ratio_test (588 words)

	Likelihood - Wikipédia
		The likelihood function does not in general follow all the axioms of probability: for example, the integral of a likelihood function is not in general 1.
		Attempting to interpret the likelihood of a hypothesis given observed evidence as the probability of the hypothesis is a common error, with potentially disastrous real-world consequences in medicine, engineering or jurisprudence.
		Likelihood as a solitary term is a shorthand for likelihood function.
	su.wikipedia.org /wiki/Likelihood (651 words)

	8.2.3.3. Likelihood ratio tests
		Calculate the maximum likelihood of the sample data based on an assumed distribution model (the maximum occurs when unknown parameters are replaced by their maximum likelihood estimates).
		Likelihood functions for reliability data are described in Section 4.
		The unrestricted likelihood of the data is the product of the two likelihoods, with 4 unknown parameters (the shape and characteristic life for each vendor population).
	www.itl.nist.gov /div898/handbook/apr/section2/apr233.htm (677 words)

	Chi-square test - Wikipedia, the free encyclopedia
		General likelihood-ratio tests are approximately chi-square tests when the sample-size is large.
		However, in cases where the exact distribution of the likelihood-ratio statistic can be easily calculated e.g., F-tests in the analysis of variance and t-tests are likelihood-ratio tests, it is more appropriate to refer to use these exact statistics.
		A chi-square test is any statistical hypothesis test in which the test statistic has a chi-square distribution if the null hypothesis is true.
	en.wikipedia.org /wiki/Chi-square_test (217 words)

	Talk:Likelihood principle - Wikipedia, the free encyclopedia
		A standard LR test, as described for example in the likelihood-ratio test article, does involve unrealized events and so it is not consistent with the likelihood principle.
		I'm willing to consider a compromise of the form "The conventional likelihood-ratio test is not consistent with the likelihood principle, although there is an unconventional LR test which is".
		A LR test appears to be similar to other null-hypothesis tests in that events that didn't happen have an effect on the inference, thus it appears to be inconsistent with the likelihood principle.
	en.wikipedia.org /wiki/Talk:Likelihood_principle (1363 words)

	DUMC Library - Likelihood Ratios
		The Likelihood Ratio (LR) is the likelihood that a given test result would be expected in a patient with the target disorder compared to the likelihood that the same result would be expected in a patient without the target disorder.
		Since sensitivity and specificity are fixed characteristics of the test itself, the likelihood ratio is independent of the prevalence of the disease in the population.
		LR is a ratio of likelihoods (or probabilities) for a given test.
	www.mclibrary.duke.edu /subject/ebm/ratios.html (568 words)

	Stata help for j_chibar
		For such tests, the distribution of the likelihood-ratio test statistic is a 50:50 mixture of chi-square distributions with k and k+1 degrees of freedom, shown on the output as "chibar(4_5)", for example.
		The likelihood ratio test that is displayed is testing on the boundary of the parameter space.
		The p-value of the LR test takes this into account, and will be set to 1 if it is determined that your estimate is close enough to zero to be, in effect, zero for purposes of significance.
	www.stata.com /help.cgi?j_chibar (367 words)

	Model discrimination, model selection, generalized likelihood ratio test - Zabel Dissertation
		The generalized likelihood ratio test (GLRT) (Mood, et al., 1974; Bickel and Doksum, 1977; Hogg and Tannis, 1983), as its name implies, is based on the ratio of the likelihoods.
		The likelihood ratio is useful because of the following result (Bickel and Doksum, 1977).
		This test can be extended to the case where the difference between the dimension of the null and alternative models is greater than 1.
	www.cqs.washington.edu /papers/zabel/chp3.doc7.html (769 words)

	The Likelihood Ratio Test
		Thus, when two models are hypothesized, the likelihood ratio test can be succinctly expressed as the comparison of the likelihood ratio with a threshold.
		The likelihood ratio test is best expressed in terms of the sufficient statistic.
		The likelihood ratio is plotted in figure 1 and the threshold value η, which is computed from the a priori probabilities and the costs to be 1/3, is indicated.
	cnx.rice.edu /content/m11234/latest (1027 words)

	Definition: Likelihood ratio
		The likelihood ratio incorporates both the sensitivity and specificity of the test and provides a direct estimate of how much a test result will change the odds of having a disease.
		The likelihood ratio of a negative test result (LR-) is 1- sensitivity divided by specificity.
		The likelihood ratio of a positive test result (LR+) is sensitivity divided by 1- specificity.
	www.childrens-mercy.org /stats/definitions/likelihood.htm (741 words)

	Likelihood Ratio Test
		The likelihood ratio test (LRT) is a statistical test of the goodness-of-fit between two models.
		In testing a molecular clock, the degrees of freedom work out to be s-2, where s is the number of taxa in the phylogeny (Felsenstein 1981).
		Using this information we can then determine the critical value of the test statistic from standard statistical tables.
	workshop.molecularevolution.org /resources/lrt.php (608 words)

	Abstract
		Robust analogues of the likelihood ratio test are considered for testing of hypotheses involving multiple discrete distributions.
		The results show that often the tests based on the ordinary and penalized distances enjoy better robustness properties than the likelihood ratio test.
		The test statistics are generalizations of the Hellinger deviance test of Simpson (1989) and disparity tests of Lindsay (1994), obtained by looking at a penalized version of the distances; Harris and Basu (1994) suggest that the penalty be based on reweighting the empty cells.
	www.math.clemson.edu /~cspark/cv/paper/m1abs.htm (135 words)

	Common Shape Parameter Likelihood Ratio Test
		The individual likelihood values for each of the test stresses can be found in the Results tab of the Likelihood Ratio Test window.
		The likelihood ratio test is performed by first obtaining the LR test statistic,
		A better assessment can be made with the LR test, which can be performed using the Likelihood Ratio Test tool in ALTA 6.
	www.weibull.com /AccelTestWeb/common_shape_parameter_likelihood_ration_test.htm (329 words)

	Ascertainment-Adjusted Maximum Likelihood Estimation for the Additive Genetic Gamma Frailty Model
		These results imply that the ascertainment-adjusted likelihood ratio test in the context of the additive genetic gamma frailty may be used for genetic linkage analysis.
		To avoid ascertainment biases in parameter estimates, retrospective likelihood ratio tests are often used, which may result in loss of efficiency due to conditioning.
		One approach is based on the likelihood function conditioning on the ascertainment event, the other is based on maximizing a full ascertainment-adjusted likelihood.
	repositories.cdlib.org /cbmb/ascertainment (256 words)

	Root and Ratio Test
		Simulating properties of the likelihood ratio test for a unit root in an explosi...
		Likelihood ratio tests for unit roots in panels...
		A likelihood ratio test for evolutionary rate shifts and functional divergence a...
	www.scienceoxygen.com /math/159.html (324 words)

	The Effects of Non-Identifiability on Testing for Detailed Balance in Aggregated Markov Models for Ion-Channel Gating -- Wagner and Timmer 79 (6): 2918 -- Biophysical Journal
		In the following, the power of the likelihood ratio test to detect violations of the law of detailed balance will be investigated.
		The power of a likelihood ratio test approaches 1 for the number of data points going to infinity (Cox and Hinkley, 1974
		FIGURE 4 Loop model: The probability to reject the null hypothesis of detailed balance against the ratio of open time constants for a test to the 5% level is shown for different values of ln K of the products of the transition rates in clockwise and counterclockwise direction.
	www.biophysj.org /cgi/content/full/79/6/2918 (4112 words)

	The Likelihood Ratio Test Procedure
		The method leads to tests called likelihood ratio tests, and although not necessarily uniformly most powerful, they often have desirable properties.
		The notion of using the magnitude of the ratio of two probability density functions as the basis of a best test or of a uniformly most powerful test can be modified, and made intuitively appealing, to provide a method of constructing a test where either or both of the hypothesis and alternative are composite.
		The test involves a comparison of the maximum value the likelihood can take when
	turing.une.edu.au /~stat354/notes/node86.html (278 words)

	g.test.Rd
		Then, log-likelihood ratio test of the null that the joint distribution of the cell counts in a 2-dimensional contingency table is the product of the row and column marginals is performed.
		In this case, the hypothesis tested is whether the population probabilities equal those in \code{p}, or are all equal if \code{p} is not given.
		\item{p.value}{the p-value for the test.} \item{method}{a character string indicating the type of test performed, and continuity correction, or Williams' chi-squared approximation was used.} \item{data.name}{a character string giving the name(s) of the data.} \item{observed}{the observed counts.} \item{expected}{the expected counts under the null hypothesis.} } \references{ Robert R. Sokal & F. James Rohlf (1995), \emph{Biometry}, 3rd ed.
	web.psych.ualberta.ca /~phurd/cruft/g.test.Rd (263 words)

	StudyGroup9 List Archive: RE: Likelihood Ratio Test
		the degrees of freedom for the likelihood ratio test is the number of
		Hogg/Klugman and Cummings likelihood ratio tests are slightly different.
		testing whether a set of groups from a population is from a distribution
	www.casact.org /lists/studygroup9/00000209.htm (421 words)

	No Title
		It says that for a given size test, the Likelihood Ratio Test will be most powerful.
		The sticky part of the proof involves handling the case where the distribution function of the likelihood ratio is not a continuous function.
		A minimax test must have a = b if it is to be admissible, so we have to find the risk point of the form (a,a) with the smallest value of a.
	www.uwm.edu /~ericskey/361material/361F98/L28/index.html (398 words)

	Chen
		The problem of testing the homogeneity in the context of finite mixture models has been discussed by many authors recently.There has been great advances in deriving the limiting distributions of the likelihood ratio test statistics for various finite mixture models.
		In this paper, we propose a modified likelihood ratio test for homogeneity in the finity mixture models of a general parametric distribution family.
		We further illustrate that the modified likelihood ratio test is far more powerful than the C(alpha) test for some finite mixture models.
	pegasus.cc.ucf.edu /~iss/Chen.html (184 words)

	Sankhya: The Indian Journal of Statistics
		The asymptotic operating characteristics of the likelihood ratio test are studied and comparisons are made between the likelihood ratio test and a Bayes test.
		In particular, the Bayes test outperforms the likelihood ratio test as long as the change point does not occur very early or late in the sequence.
		It is shown, using a result of Darling and Erdos, that the likelihood ratio, suitably normalized and under H
	sankhya.isical.ac.in /search/48a3/48a3008.htm (172 words)

	C Zhang Abstract
		Maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting.
		We introduce the generalized likelihood statistics to overcome the drawbacks of nonparametric maximum likelihood ratio statistics.
		Maximum likelihood ratio theory contributes tremendous success to parametric inferences, due to the fundamental theory of Wilks (1938).
	www.stat.unc.edu /abstracts/czhang.html (169 words)

	Welcome to Sanat K. Sarkar's Website!
		“A likelihood ratio test and its modifications for the homogeneity of the covariance matrices of dependent multivariate normals”.
		“The likelihood ratio test for the homogeneity of the variances in a covariance matrix with block compound symmetry.” Communications in Statsitics – Theory and Methods, 29, 1155-1178.
		“Unbiasedness of the likelihood ratio test for sphericity with a general pattern of sample.” Cal. Statist.
	www.sbm.temple.edu /~sanat/publications.html (737 words)

	Criteria in Hypothesis Testing
		This statement is obvious as we minimized the probability of error in deriving the likelihood ratio test.
		This expression for the likelihood ratio is complicated.
		Furthermore, these expressions point out that the likelihood ratio and the sufficient statistic can be considered a function of the observations r; hence, they are random variables and have probability densities for each model.
	cnx.rice.edu /content/m11228/latest (1637 words)

	PG-IV: P297 - Maximum Likelihood Gene Ordering
		Another argument against the likelihood approach is that the likelihood comparison cannot be implemented as the formerly log likelihood ratio test because there is no degree of freedom difference for the parameters among the possible locus orders.
		For gene ordering problem, if the parameters for the data are sufficient and the maximum likelihood estimates of the parameters are unbiased for different orders, the log likelihoods evaluated using the maximum likelihood estimates should be same for all possible gene orders.
		When a perfect model is used for a mapping data set, the log likelihoods should be same for all possible locus orders for the same data set.
	www.intl-pag.org /pag/4/abstracts/p297.html (232 words)

	A likelihood ratio test for evolutionary rate shifts and functional divergence among proteins -- Knudsen and Miyamoto 98 (25): 14512 -- Proceedings of the National Academy of Sciences
		A likelihood ratio test for evolutionary rate shifts and functional divergence among proteins -- Knudsen and Miyamoto 98 (25): 14512 -- Proceedings of the National Academy of Sciences
		A likelihood ratio test for evolutionary rate shifts and functional divergence among proteins
		To test whether a site from two related groups of sequences is evolving differently, the positions are analyzed individually.
	www.pnas.org /cgi/content/full/98/25/14512 (4483 words)

	Likelihood Ratio Test for the Equivalence of Two Autoregressive Moving- Average Time Series - Storming Media
		Monte Carlo analysis has shown that the likelihood ratio test has a good fit to the chi square distribution, with degrees of freedom equal to the number of parameters being tested.
		Specifically, a likelihood ratio test for the equivalence of two autoregressive moving average (ARMA) time series is derived.
		Four cases of this test are presented for examining the ARMA parameters, series means, and/or innovations variances.
	www.stormingmedia.us /99/9950/A995073.html (208 words)

	A Likelihood Ratio Test Against Stochastic Ordering in Several Populations (ResearchIndex)
		For testing equality of distributions against a stochastic ordering in several populations, this paper derives the null asymptotic distribution of the likelihood ratio test statistic, which is characterized by minimization problems and has no closed form.
		Abstract: The likelihood ratio test is often used to test hypotheses involving a stochastic ordering.
		Asymptotic Expansions Of The Likelihood Ratio Test Statistic..
	citeseer.ist.psu.edu /wang96likelihood.html (490 words)

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