Composite likelihood inference by nonparametric saddlepoint tests
Copyright policy )Composite likelihood inference by nonparametric saddlepoint tests
The class of composite likelihood functions provides a flexible and powerful toolkit to carry out approximate inference for complex statistical models when the full likelihood is either impossible to specify or unfeasible to compute. However, the strenght of the composite likelihood approach is dimmed when considering hypothesis testing about a multidimensional parameter because the finite sample behavior of likelihood ratio, Wald, and score-type test statistics is tied to the Godambe information matrix. Consequently inaccurate estimates of the Godambe information translate in inaccurate p-values. In this paper it is shown how accurate inference can be obtained by using a fully nonparametric saddlepoint test statistic derived from the composite score functions. The proposed statistic is asymptotically chi-square distributed up to a relative error of second order and does not depend on the Godambe information. The validity of the method is demonstrated through simulation studies.
- University of Milano-Bicocca Italy
- University of Padua Italy
- University of Geneva Switzerland
- University of Trieste Italy
- Ca Foscari University of Venice Italy
FOS: Computer and information sciences, Pairwise likelihood, small sample inference, relative error, Mathematics - Statistics Theory, Statistics Theory (math.ST), Nonparametric inference, 310, saddlepoint test, Methodology (stat.ME), empirical likelihood methods, Empirical likelihood methods, nonparametric inference, Relative error Robust tests Saddlepoint test Small sample inference, FOS: Mathematics, robust tests, Statistics - Methodology, Empirical likelihood methods, Godambe information, Likelihood ratio adjustment, Nonparametric inference, Pairwise likelihood, Relative error, Robust tests, Saddlepoint test, Small sample inference, Empirical likelihood methods; Godambe information; Likelihood ratio adjustments; Nonparametric inference; Pairwise likelihood; Relative error; Robust tests; Saddlepoint test; Small sample inference, Empirical likelihood methods; Godambe information; Likelihood ratio adjustments; Nonparametric inference; Pairwise likelihood; Relative error; Robust tests; Saddlepoint test; Small sample inference;, Computational methods for problems pertaining to statistics, likelihood ratio adjustments, pairwise likelihood, 62G10, 62G35, Likelihood ratio adjustments, Godambe information
FOS: Computer and information sciences, Pairwise likelihood, small sample inference, relative error, Mathematics - Statistics Theory, Statistics Theory (math.ST), Nonparametric inference, 310, saddlepoint test, Methodology (stat.ME), empirical likelihood methods, Empirical likelihood methods, nonparametric inference, Relative error Robust tests Saddlepoint test Small sample inference, FOS: Mathematics, robust tests, Statistics - Methodology, Empirical likelihood methods, Godambe information, Likelihood ratio adjustment, Nonparametric inference, Pairwise likelihood, Relative error, Robust tests, Saddlepoint test, Small sample inference, Empirical likelihood methods; Godambe information; Likelihood ratio adjustments; Nonparametric inference; Pairwise likelihood; Relative error; Robust tests; Saddlepoint test; Small sample inference, Empirical likelihood methods; Godambe information; Likelihood ratio adjustments; Nonparametric inference; Pairwise likelihood; Relative error; Robust tests; Saddlepoint test; Small sample inference;, Computational methods for problems pertaining to statistics, likelihood ratio adjustments, pairwise likelihood, 62G10, 62G35, Likelihood ratio adjustments, Godambe information
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