Likelihood ratio statistics based on an integrated likelihood

An integrated likelihood depends only on the parameter of interest and the data, so it can be used as a standard likelihood function for likelihood-based inference. In this paper, the higher-order asymptotic properties of the signed integrated likelihood ratio statistic for a scalar parameter of interest are considered. These results are used to construct a modified integrated likelihood ratio statistic and to suggest a class of prior densities to use in forming the integrated likelihood. The properties of the integrated likelihood ratio statistic are compared to those of the standard likelihood ratio statistic. Several examples show that the integrated likelihood ratio statistic can be a useful alternative to the standard likelihood ratio statistic. Copyright 2010, Oxford University Press.

[1]  Andrew L. Rukhin,et al.  Tools for statistical inference , 1991 .

[2]  Toshihide Kitakado,et al.  An Integrated-Likelihood Method for Estimating Genetic Differentiation Between Populations , 2006, Genetics.

[3]  Brunero Liseo,et al.  Elimination of nuisance parameters with reference priors , 1993 .

[4]  R. Mukerjee.  Conditional likelihood and power: higher-order asymptotics , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[5]  G. Chamberlain.  Decision Theory Applied to an Instrumental Variables Model , 2007 .

[6]  Abraham Wald,et al.  Statistical Decision Functions , 1951 .

[7]  Trevor J. Sweeting,et al.  Approximate Bayesian computation based on signed roots of log-density ratios (with discussion) , 1996 .

[8]  R. Redner,et al.  Estimation of Linkage and Association from Allele Transmission Data , 2003 .

[9]  O. E. Barndorff-Nielsen,et al.  Infereni on full or partial parameters based on the standardized signed log likelihood ratio , 1986 .

[10]  D. Cox,et al.  Analysis of Survival Data. , 1985 .

[11]  O. Barndorff-Nielsen.  On a formula for the distribution of the maximum likelihood estimator , 1983 .

[12]  Malene Højbjerre,et al.  Profile likelihood in directed graphical models from BUGS output , 2003, Stat. Comput..

[13]  H. W. Peers.  Likelihood ratio and associated test criteria , 1971 .

[14]  Harrison H. Barrett,et al.  Foundations of Image Science , 2003, J. Electronic Imaging.

[15]  Donald Fraser,et al.  Likelihood for component parameters , 2003 .

[16]  Malay Ghosh,et al.  Likelihood-based Inference for the Ratios of Regression Coefficients in Linear Models , 2006 .

[17]  T. Severini.  Likelihood Methods in Statistics , 2001 .

[18]  Adrian F. M. Smith,et al.  Bayesian Statistics 5. , 1998 .

[19]  T. Severini.  Integrated likelihood functions for non-Bayesian inference , 2007 .

[20]  D. Cox,et al.  Inference and Asymptotics , 1994 .

[21]  Trevor J. Sweeting,et al.  On the implementation of local probability matching priors for interest parameters , 2005 .

[22]  Thomas A. Severini,et al.  An empirical adjustment to the likelihood ratio statistic , 1999 .

[23]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[24]  O. Barndorff-Nielsen.  Stable and invariant adjusted profile likelihood and directed likelihood for curved exponential models , 1995 .

[25]  J. Pfanzagl,et al.  An asymptotically complete class of tests , 1978 .

[26]  Luigi Pace,et al.  The directed modified profile likelihood in models with many nuisance parameters , 1999 .

[27]  Trevor J. Sweeting,et al.  A framework for Bayesian and likelihood approximations in statistics , 1995 .

[28]  Thomas J. DiCiccio,et al.  Simple Modifications for Signed Roots of Likelihood Ratio Statistics , 1993 .

[29]  Nancy Reid,et al.  Adjustments to profile likelihood , 1989 .

[30]  R. Tibshirani.  Noninformative priors for one parameter of many , 1989 .

[31]  Donald A. Pierce,et al.  Practical Use of Higher Order Asymptotics for Multiparameter Exponential Families , 1992 .

[32]  D. Cox,et al.  Parameter Orthogonality and Approximate Conditional Inference , 1987 .

[33]  Tim B. Swartz,et al.  Approximating Integrals Via Monte Carlo and Deterministic Methods , 2000 .

[34]  R. Mukerjee,et al.  Probability Matching Priors: Higher Order Asymptotics , 2004 .

[35]  I. Skovgaard,et al.  An explicit large-deviation approximation to one-parameter tests , 1996 .

[36]  R. Wolpert,et al.  Integrated likelihood methods for eliminating nuisance parameters , 1999 .