Abstract
In this paper, we adopt the point of view of a decision-maker who evaluates a probabilistic model based on the test-sample averaged utility of the expected-utility optimal strategy that the model suggests in a horse race setting. After briefly reviewing the basic properties of the resulting performance measure for probabilistic models, we show that such a measure ranks two models according to their likelihood ratio if and only if the performance measure is based on a generalized logarithmic utility function. Thus, we provide a new decision theoretic motivation of the likelihood ratio as a model performance measure.
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References
G. A. Barnard. Statistical inference (with discussion). Journal of the Royal Statistical Society, B, 11:115, 1949.
J. M. Bernardo. Expected information as expected utility. Annals of Statistics, 7:686–690, 1979.
J. M. Bernardo and A. F. M. Smith. Bayesian Theory. Wiley, New York, 2000.
D. Bernoulli. Specimen theoriae novae de mensura sortis, Commentarii Academiae Scientiarum Imperialis Petropolitanae (5, 175–192, 1738). Econometrica, 22:23–36, 1954, 1738. Translated by L. Sommer.
A. Birnbaum. On the foundation of statistical inference (with discussion). J. Am. Stat. Assoc., 69:269, 1962.
T. Cover and J. Thomas. Elements of Information Theory. Wiley, New York, 1991.
R. A. Fisher. On the mathematical foundation of theoretical statistics. Philosophical Transactions of the Royal Society of London, A, 222:309, 1922.
C. Friedman and S. Sandow. Model performance measures for expected utility maximizing investors. International Journal of Theoretical and Applied Finance, 6(4):355, 2003.
E. T. Jaynes. Probability Theory. The Logic of Science. Cambridge University Press, Cambridge, 2003.
D. Luenberger. Investment Science. Oxford University Press, New York, 1998.
J. Neyman and E. S. Pearson. On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London, A, 231:289, 1933.
M. Rubinstein. The strong case for the generalized logarithmic utility as the premier model of financial markets. Journal of Finance, May, 1976.
L. J. Savage. Elicitation of personal probabilities and expectations. Journal of the American Statistical Association, 66:783–801, 1971.
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Friedman, C., Sandow, S. Utility functions that lead to the likelihood ratio as a relative model performance measure. Statistical Papers 47, 211–225 (2006). https://doi.org/10.1007/s00362-005-0284-5
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DOI: https://doi.org/10.1007/s00362-005-0284-5