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Composite Likelihood Inference by Nonparametric Saddlepoint Tests

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  • Lunardon, Nicola
  • Ronchetti, Elvezio
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    Abstract

    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 strength 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.

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    File URL: http://hdl.handle.net/10077/8806
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    Bibliographic Info

    Paper provided by DEAMS - Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche "Bruno de Finetti" in its series Working Papers DEAMS with number 12.

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    Date of creation: Jun 2013
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    Handle: RePEc:tre:wpaper:12

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    Keywords: Empirical likelihood methods; Godambe information; Likelihood ratio adjustment; Nonparametric inference; Pairwise likelihood; Relative error; Robust tests; Saddlepoint test; Small sample inference;

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