Composite likelihood inference for ordinal periodontal data with replicated spatial patterns

We describe a prototype approach to flexible modelling for maxima observed at sites in a spatial domain, based on fitting of max-stable processes derived from underlying Gaussian random fields. The models we propose have generalized extreme-value marginal distributions throughout the spatial domain, consistent with statistical theory for maxima in simpler cases, and can incorporate both geostatistical correlation functions and random set components. Parameter estimation and fitting are performed through composite likelihood inference applied to observations from pairs of sites, with occurrence times of maxima taken into account if desired, and competing models are compared using appropriate information criteria. Diagnostics for lack of model fit are based on maxima from groups of sites. The approach is illustrated using annual maximum temperatures in Switzerland, with risk analysis proposed using simulations from the fitted max-stable model. Drawbacks and possible developments of the approach are discussed.

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Spatial composite likelihood inference using local C-vines

Journal of Multivariate Analysis ◽

10.1016/j.jmva.2015.01.021 ◽

2015 ◽

Vol 138 ◽

pp. 74-88 ◽

Cited By ~ 19

Author(s):

Tobias Michael Erhardt ◽

Claudia Czado ◽

Ulf Schepsmeier

Keyword(s):

Composite Likelihood ◽

Likelihood Inference

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On specification tests for composite likelihood inference

Biometrika ◽

10.1093/biomet/asaa039 ◽

2020 ◽

Vol 107 (4) ◽

pp. 907-917

Author(s):

Jing Huang ◽

Yang Ning ◽

Nancy Reid ◽

Yong Chen

Keyword(s):

Likelihood Function ◽

Complex Structure ◽

Information Matrix ◽

Composite Likelihood ◽

Likelihood Inference ◽

Test Statistics ◽

Finite Sample ◽

Sensitivity Matrix ◽

Specification Tests ◽

Local Alternative

Summary Composite likelihood functions are often used for inference in applications where the data have a complex structure. While inference based on the composite likelihood can be more robust than inference based on the full likelihood, the inference is not valid if the associated conditional or marginal models are misspecified. In this paper, we propose a general class of specification tests for composite likelihood inference. The test statistics are motivated by the fact that the second Bartlett identity holds for each component of the composite likelihood function when these components are correctly specified. We construct the test statistics based on the discrepancy between the so-called composite information matrix and the sensitivity matrix. As an illustration, we study three important cases of the proposed tests and establish their limiting distributions under both null and local alternative hypotheses. Finally, we evaluate the finite-sample performance of the proposed tests in several examples.

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A note on composite likelihood inference and model selection

Biometrika ◽

10.1093/biomet/92.3.519 ◽

2005 ◽

Vol 92 (3) ◽

pp. 519-528 ◽

Cited By ~ 172

Author(s):

Cristiano Varin ◽

Paolo Vidoni

Keyword(s):

Model Selection ◽

Composite Likelihood ◽

Likelihood Inference

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