The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses

By S. S. Wilks. 1938

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Citations in the corpus

Identification of b-quark jets with the CMS experiment (2012, background): “The distribution of −2 ln(LR(SFb)) is asymptotically distributed as a χ2 distribution with one degree of freedom (Wilk’s theorem [44]).”
Dark photon limits: A handbook (2021, background): “ing to a χ(2)2 distribution since the models differ by two parameters [227].”
The likelihood ratio test for homogeneity in finite mixture models (2001, methodology): “Note that -r2, = -2 { (0, 00, 0) - n (0, 0, 0) } is an ordinary likelihood ratio (no mixtures involved) and hence an approximation is immediate as follows (Wilks 1938):”
Dark matter and pulsar model constraints from Galactic Center Fermi-LAT gamma-ray observations (2013, background): “In the large sample limit, under the no source hypothesis, TS has a χ(2)/2 distribution with the number of degrees of freedom equal to the number of parameters associated with the proposed positive amplitude new source [24, 25] which in this case is two for position, one for amplitude, and one for s”
The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference. (2014, methodology): “As a likelihood ratio test, standard large-sample theory (Wilks, 1938; Wald, 1943) applies to the time-domain G-causality estimator in both the conditional and unconditional cases.”
A modified likelihood ratio test for homogeneity in finite mixture models (2001, unknown): “The LRT has a simple interpretation, is invariant under re-parameterization and, under standard regularity conditions, has a simple and elegant asymptotic theory (Wilks, 1938).”
An Indication of Anisotropy in Arrival Directions of Ultra-high-energy Cosmic Rays through Comparison to the Flux Pattern of Extragalactic Gamma-Ray Sources (2018, methodology): “For a given energy threshold, we confirmed with simulations that the TS for isotropy follows a 2c distribution with two degrees of freedom, as expected (Wilks 1938), directly accounting for the fit of two parameters of the model.”
Improving marginal likelihood estimation for Bayesian phylogenetic model selection. (2011, methodology): “…likelihood measures the average fit of a model to the data, whereas traditional approaches to model selection, such as likelihood ratio tests (LRT; Wilks 1938), the Akaike Information Criterion (AIC; Akaike 1974), the Bayesian Information Criterion (BIC; Schwarz 1978), and the decision-theoretic…”
Nonparametric inference in generalized functional linear models (2014, methodology): “As seen above, the null limiting distribution has the nice property that it is free of the unknown model parameters, that is, so-called Wilks phenomenon [11, 33].”
Two-sample Bayesian Nonparametric Hypothesis Testing (2009, background): “It follows that, underHj0,−2 logLj asymptotically follows a χ2 distribution (Wilks, 1938).”
Unsupervised Generative Modeling Using Matrix Product States (2017, methodology): “The reason for adopting this statistic is that it is asymptotically χ(2)-distributed [49].”
Data exploration, quality control and testing in single-cell qPCR-based gene expression experiments (2012, unknown): “Applying classical asymptotic results about LRTs (Wilks, 1938), 2 log ðy, vÞ converges to a 2 distribution with two degrees of freedom under H0.”
The Higgs boson machine learning challenge (2014, background): “According to Wilks’ theorem (Wilks, 1938), given that certain regularity conditions are satisfied, the test statistic”
Estimating the rate of molecular evolution: incorporating non-contemporaneous sequences into maximum likelihood phylogenies (2000, background): “Twice the difference of the log likelihoods (2 ) is expected to be χ2 distributed with degrees of freedom equal to the difference in the number of free parameters between the models we are comparing (Wilks, 1938).”
Likelihood based inference for monotone response models (2007, background): “In particular, the emergence of a fixed limit law for the pointwise likelihood ratio statistic for testing ˆ has some of the flavor of Wilks’ classical result ( Wilks (1938) ) on the limiting ´2 distribution of likelihood ratios in standard parametric models.”
Log‐symmetric quantile regression models (2020, methodology): “The second simulation analyzes the performance of the gradient (Terrell, 2002), likelihood ratio (Wilks, 1938), score (Rao, 1948), and Wald (Wald, 1947) tests.”