Abstract
In this article we describe an extension based on relevance weighting of Wald’s classical likelihood theory. The extension allows bias to be traded for precision in the likelihood setting like bias is traded for variance in nonparametric regression. All relevant sample information can thereby be used while bias is filtered out. We describe and demonstrate the use of both the nonparametric and parametric likelihoods. The latter is used to develop a method for forecasting goals in ice-hockey.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
7 References
Akaike, H. (1973). Information theory and an extension of entropy maximization principle. In B. Petrov and F. Csak (Eds.), 2nd International Symposium on Information Theory, pp. 276–281. Kiado: Akademia.
Akaike, H. (1977). On entropy maximization principle. In P. Krishnaiah (Ed.), Applications of Statistics, pp. 27–41. Amsterdam: North-Holland.
Akaike, H. (1978). A Bayesian analysis if the minimum aie procedure. Ann. Inst. Statist. Math. 30A, 9–14.
Akaike, H. (1982). On the fallacy of the likelihood principle. Statist. Probab. Lett. 1, 75–78.
Akaike, H. (1983). Information measures and model selection. Bull. Inst. Internat. Statist. 50, 277–291.
Akaike, H. (1985). Prediction and entropy. In A celebration of statistics, pp. 1–24. New York-Berlin: Springer.
Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis, Second edition. New York: Springer-Verlag.
Chung, K.L. (1968). A Course in Probability Theory. New York: Harcourt Brace and World, Inc.
Efron, B. (1996). Empirical Bayes methods for combining likelihoods (with discussion). J. Amer. Statist. Assoc. 91, 538–565.
Fan, J., N.E. Heckman, and W.P. Wand (1995). Local polynomial kernel regression for generalized linear models and quasi-likelihood functions. J. Amer. Statist. Assoc. 90, 826–838.
Hoeffding, W. (1963). Probability inequalities for sum of bounded random variables. J. Amer. Statist. Assoc. 58, 13–30.
Hu, F. (1994). Relevance weighted smoothing and a new bootstrap method. Technical report, Department of Statistics, University of British Columbia.
Hu, F. (1997). Asymptotic properties of relevance weighted likelihood estimations. Canad. J. Statist. 25, 45–60.
Hu, F. and J.V. Zidek (1993). A relevance weighted quantile estimator. Technical report, Department of Statistics, University of British Columbia.
Hu, F. and J.V. Zidek (1997). The relevance weighted likelihood. Unpublished.
Koul, H.L. (1992). Weighted Empiricals and Linear Models, Volume 21 of IMS Lecture Notes. Hayward, CA: Inst. Math. Statist.
Marcus, M.B. and J. Zinn (1984). The bounded law of the iterated logarithm for the weighted empirical distribution process in the non-iid case. Ann. Prob. 12, 335–360.
Shorack, G.R. and J.A. Wellner (1986). Empirical Processes with Applications to Statistics. New York: Wiley.
Staniswalis, J.G. (1989). The kernel estimate of a regression function in likelihood-based models. J. Amer. Statist. Assoc. 84, 276–283.
Tibshirani, R. and T. Hastie (1987). Local likelihood estimation. J. Amer. Statist. Assoc. 82, 559–567.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Hu, F., Zidek, J.V. (2001). The Relevance Weighted Likelihood With Applications. In: Ahmed, S.E., Reid, N. (eds) Empirical Bayes and Likelihood Inference. Lecture Notes in Statistics, vol 148. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0141-7_13
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0141-7_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95018-1
Online ISBN: 978-1-4613-0141-7
eBook Packages: Springer Book Archive