Abstract
The possibility that the conditional maximum likelihood estimator (CMLE) is superior to the unconditional maximum likelihood estimator (UMLE) is discussed in examples where the residual likelihood is obstructive. We observe relatively smaller risks of the CMLE for a finite sample size. The models in the study include the normal, inverse Gauss, gamma, two-parameter exponential, logit, negative binomial and two-parameter geometric ones.
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References
Andersen, E. B. (1970). Asymptotic properties of conditional maximum-likelihood estimators, J. Roy. Statist. Soc. Ser. B, 32, 283–301.
Anraku, K. and Yanagimoto, T. (1988). Estimation for the negative binomial distribution based on the conditional likelihood, Research Memorandum, No. 349, The Institute of Statistical Mathematics.
Bar-Lev, S. K. (1984). Asymptotic behaviour of conditional maximum likelihood estimators in a certain exponential model, J. Roy. Statist. Soc. Ser. B, 46, 425–430.
Barndorff-Nielsen, O. (1978) Information and Exponential Families in Statistical Theory, Wiley, New York.
Barndorff-Nielsen, O. (1980). Conditionality resolutions, Biometrika, 67, 293–310.
Blaesild, P. and Jensen, J. L. (1985). Saddiepoint formulas for reproductive exponential models, Scand. J. Statist., 12, 193–202.
Bliss, C. I. and Owen, A. R. G. (1958). Negative binomial distributions with a common k, Biometrika, 45, 37–58.
Breslow, N. E. and Cologne, J. (1986). Methods of estimation in log odds ratio regression models, Biometrics, 42, 949–954.
Dawid, A. P. (1975). On the concepts of sufficiency and ancillarity in the presence of nuisance parameters, J. Roy. Statist. Soc. Ser. B, 37, 248–258.
Fisher, R. A. (1935). The logic of inductive inference, J. Roy. Statist. Soc., 98, 39–54.
Godambe, V. P. (1976). Conditional likelihood and unconditional optimum estimating equations, Biometrika, 63, 277–284.
Godambe, V. P. (1980). On sufficiency and ancillarity in the presence of a nuisance parameter, Biometrika, 67, 155–162.
Hauck, W. W., Anderson, S. and Leahy, F. J. (1982). Finite-sample properties of some old and some new estimators of a common odds ratio from multiple 2×2 tables, J. Amer. Statist. Assoc., 77, 145–152.
Kalbfleisch, J. D. and Sprott, D. A. (1970). Application of likelihood methods to models involving large numbers of parameters (with discussions), J. Roy. Statist. Soc. Ser. B, 32, 175–208.
Kalbfleisch, J. D. and Sprott, D. A. (1973). Marginal and conditional likelihoods, Sankhya Ser. A, 35, 311–328.
Lindsay, B. (1982). Conditional score functions: Some optimality results, Biometrika, 69, 503–512.
Lubin, J. H. (1981). An empirical evaluation of the use of conditional and unconditional likelihoods for case-control data, Biometrika, 68, 567–571.
Nelder, J. A. and Wedderburn, R. W. M. (1972). Generalized linear model (with discussion), J. Roy. Statist. Soc. Ser. A, 34, 370–384.
Neyman, J. and Scott, E. L. (1948). Consistent estimates based on partially consistent observations, Econometrica, 16, 1–32.
Yanagimoto, T. (1987). A notion of an obstructive residual likelihood, Ann. Inst. Statist. Math., 39, 247–261.
Yanagimoto, T. (1988a). The conditional maximum likelihood estimator of the shape parameter in the gamma distribution, Metrika, 35, 161–175.
Yanagimoto, T. (1988b). The conditional MLE in the two-parameter geometric distribution and its competitors, Comm. Statist. A—Theory Methods, 17, 2779–2787.
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Yanagimoto, T., Anraku, K. Possible superiority of the conditional MLE over the unconditional MLE. Ann Inst Stat Math 41, 269–278 (1989). https://doi.org/10.1007/BF00049395
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DOI: https://doi.org/10.1007/BF00049395