Asymptotics for likelihood ratio tests under loss of identifiability

By Xin Liu, Yongzhao Shao. 2003

194 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ef591fd0b95f553c8e54c27a3f7e272937271f67

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Sensitivity Analysis in Semiparametric Likelihood Models (2011, methodology): “Under a key assumption that the class of generalized score functions {sD(·; θ) : θ ∈ Θ, 0 < D(θ, θ0) ≤ δ} is Donsker in L2(PZ) for a small δ > 0, Liu and Shao (2003) establish that D(θ̂, θ0) = OPZ ( n−1/2 ) and LR(θ0) = 2[Ln(θ̂) − Ln(θ0)] = OPZ (1), which is then used to obtain the asymptotic null…”
Bayesian Analysis in Moment Inequality Models (2010, background): “Let θ∗ = θ2, R∗ = R4 .”
Testing the Number of Components in Normal Mixture Regression Models (2015, background): “Liu and Shao (2003) analyze the LRT statistic of mixture models without a structural parameter.”
ESTIMATION AND INFERENCE WITH WEAK, SEMI-STRONG, AND STRONG IDENTIFICATION (2010, unknown): “…abrupt transition threshold autoregressive models are not covered by the results of the present paper; for example, see Picard (1985), Chan (1993), Bai (1997), Hansen (2000), Liu and Shao (2003), Elliott and Müller (2007, 2008), Qu and Perron (2007), and Drton (2009) for analyses of these models.”
Testing for Threshold Effects in Regression Models (2010, background): “The standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function (see, e.g., Andrews, 2001; Liu and Shao, 2003; Zhu and Zhang, 2006; Song et al., 2009).”
Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices (2009, methodology): “It is known that the likelihood ratio statistic has a nonstandard limiting distribution when applied to testing the number of components of a mixture model (see, for example, Liu and Shao (2003)).”
Hypothesis test for normal mixture models: The EM approach (2009, background): “In Hartigan (1985), Liu, Pasarica and Shao (2003) and Liu and Shao (2004), the likelihood ratio statistic is shown to diverge to infinity as the sample size increases, which forces most researchers to restrict the mixing parameter (θ) into some compact space.”
Model selection in high dimensions: a quadratic‐risk‐based approach (2006, background): “As mentioned earlier, a comparison of the non-parametric risk and the parametric risk gives a global assessment of model quality.”
A Bayesian information criterion for singular models (2013, methodology): “Keywords: Bayesian information criterion; Factor analysis; Mixture model; Model selection; Reduced rank regression; Schwarz information criterion; Singular learning theory”
On strong identifiability and convergence rates of parameter estimation in finite mixtures (2016, unknown): “Example 2.2.”
A Test of Non-Identifying Restrictions and Confidence Regions for Partially Identified Parameters (2009, unknown): “Also related is the analysis in Liu and Shao (2003) of the AC C EP TE D M AN U SC R IP T likelihood ratio test when the likelihood is maximized on a set as opposed to a single point.”
Testing the Order of a Finite Mixture (2010, background): “This forces most researchers to restrict the parameter space to a compact space, under which the limiting distributions of the LRT are presented as functions of the supremum of Gaussian processes (see, e.g., Ghosh and Sen 1985; Chernoff and Lander 1995; Dacunha-Castelle and Gassiat 1999; Chen and Ch”
Inference on the Order of a Normal Mixture (2012, background): “DacunhaCastelle and Gassiat (1999) and Liu and Shao (2003) obtained © 2012 American Statistical Association Journal of the American Statistical Association September 2012, Vol. 107, No. 499, Theory and Methods DOI: 10.1080/01621459.2012.695668 1096 the limiting distribution of the likelihood ratio…”
Discrete games with flexible information structures: an application to local grocery markets (2014, methodology): “To relax the assumption that the model is point identified, Liu and Shao (2003) derive the asymptotic distribution in the set-identified case under generalized regularity conditions that use the Hellinger distance between probability distributions rather than the Euclidean distance in Θ as the basis”