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Combining Likelihood Information from Independent Investigations

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ABSTRACT
Fisher [1] proposed a simple method to combine p-values from independent investigations without using detailed information of the original data. In recent years, likelihood-based asymptotic methods have been developed to produce highly accurate p-values. These likelihood-based methods generally required the likelihood function and the standardized maximum likelihood estimates departure calculated in the canonical parameter scale. In this paper, a method is proposed to obtain a p-value by combining the likelihood functions and the standardized maximum likelihood estimates departure of independent investigations for testing a scalar parameter of interest. Examples are presented to illustrate the application of the proposed method and simulation studies are performed to compare the accuracy of the proposed method with Fisher’s method.
 
Cite this paper
Jiang, L. and Wong, A. (2015) Combining Likelihood Information from Independent Investigations. Open Journal of Statistics, 5, 51-59. doi: 10.4236/ojs.2015.51007.
 
References
[1]Fisher, R.A. (1925) Statistical Methods for Research Workers. Oliver and Boyd, Edinburg.
 
[2]Lugannani, R. and Rice, S. (1980) Saddlepoint Approximation for the Distribution of the Sum of Independent Random Variables. Advances in Applied Probability, 12, 475-490.
http://dx.doi.org/10.2307/1426607
 
[3]Barndorff-Nielsen, O.E. (1986) Inference on Full or Partial Parameters Based on the Standardized Log Likelihood Ratio. Biometrika, 73, 307-322.
 
[4]Barndorff-Nielsen, O.E. (1991) Modified Signed Log-Likelihood Ratio. Biometrika, 78, 557-563.
http://dx.doi.org/10.1093/biomet/78.3.557
 
[5]Fraser, D.A.S. and Reid, N. (1995) Ancillaries and Third Order Significance. Utilitas Mathematica, 47, 33-53.
 
[6]Fraser, D.A.S. (1990) Tail Probabilities from Observed Likelihoods. Biometrika, 77, 65-76.
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[7]Jensen, J.L. (1992) The Modified Signed Log Likelihood Statistic and Saddlepoint Approximations. Biometrika, 79, 693-704.
http://dx.doi.org/10.1093/biomet/79.4.693
 
[8]Brazzale, A.R., Davison, A.C. and Reid, N. (2007) Applied Asymptotics: Case Studies in Small-Sample Statistics. Cambridge University Press, New York.
http://dx.doi.org/10.1017/CBO9780511611131
 
[9]Fraser, D.A.S. and Reid, N. (2001) Ancillary Information for Statistical Snference, Empirical Bayes and Likelihood Inference. Springer-Verlag, New York, 185-209.
http://dx.doi.org/10.1007/978-1-4613-0141-7_12
 
[10]Reid, N. and Fraser, D.A.S. (2010) Mean Likelihood and Higher Order Inference. Biometrika, 97, 159-170.
http://dx.doi.org/10.1093/biomet/asq001
 
[11]Davison, A.C., Fraser, D.A.S. and Reid, N. (2006) Improved Likelihood Inference for Discrete Data. Journal of the Royal Statistical Society Series B, 68, 495-508.
http://dx.doi.org/10.1111/j.1467-9868.2006.00548.x
 
[12]Fraser, A.M., Fraser, D.A.S. and Fraser, M.J. (2010) Parameter Curvature Revisited and the Bayesian Frequentist Divergence. Journal of Statistical Research, 44, 335-346.
 
[13]Jeffreys, H. (1946) An Invariant Form for the Prior Probability in Estimation Problems. Proceedings of the Royal Society of London Series A: Mathematical and Physical Sciences, 186, 453-461.
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[14]DiCiccio, T., Field, C. and Fraser, D.A.S. (1989) Approximations of Marginal Tail Probabilities and Inference for Scalar Parameters. Biometrika, 77, 77-95.
http://dx.doi.org/10.1093/biomet/77.1.77                                                   eww150225lx
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