Pitman closeness criterion

In statistical theory, the Pitman closeness criterion, named after E. J. G. Pitman, is a way of comparing two candidate estimators for the same parameter. Under this criterion, estimator A is preferred to estimator B if the probability that estimator A is closer to the true value than estimator B is greater than one half. Here the meaning of closer is determined by the absolute difference in the case of a scalar parameter, or by the Mahalanobis distance for a vector parameter.

References

• Pitman, E. (1937) "The “closest” estimates of statistical parameters". Mathematical Proceedings of the Cambridge Philosophical Society, 33 (2), 212–222. doi:10.1017/S0305004100019563
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• Peddada, D. S. (1985) "A short note on Pitman’s measure of nearness". American Statistician, 39, 298–299.
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• Fountain, R. L. (1991) "Pitman closeness comparison of linear estimators: A canonical form", Commun. Statist.–Theory Meth., 20 (11), 3535–3550.
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• Johnson, N. L. (1950) "On the comparison of estimators", Biometrika, 37, 281–287. JSTOR 2332381
• Keating, J. P.; Gupta, R. C. (1984) "Simultaneous comparison of scale estimators". Sankhya, Ser. B 46, 275–280. JSTOR 25052351
• Keating, J. P.; Mason, R. L.; Sen, P. K. (1993) Pitman’s Measure of Closeness: A Comparison of Statistical Estimators, SIAM, Philadelphia. ISBN:9780898713084
• Kubokawa, T. (1991) "Equivariant estimation under the Pitman closeness criterion". Commun. Statist.–Theory Meth., 20 (11), 3499–3523. doi:10.1080/03610929108830721
• Lee, C. (1990) "On the characterization of Pitman’s measure of nearness". Statistics and Probability Letters, 8, 41–46.
• Robert, Christian P.; Hwang, J. T. Gene; Strawderman, William E. (1993) "Is Pitman Closeness a Reasonable Criterion?", Journal of the American Statistical Association, 57–63 JSTOR 2290692
• Blyth, C. R. (1993) "Is Pitman Closeness a Reasonable Criterion?: Comment", Journal of the American Statistical Association, 88 421), 72–74.
• Casella, G. ; Wells, M. T. (1993) "Is Pitman Closeness a Reasonable Criterion?: Comment", Journal of the American Statistical Association, 70–71.
• Ghosh, M., Keating, J. P. and Sen, P. K. (1993) "Is Pitman Closeness a Reasonable Criterion?: Comment", Journal of the American Statistical Association, 88, 63–66.
• Peddada, S. D. (1993) "Is Pitman Closeness a Reasonable Criterion?: Comment", Journal of the American Statistical Association, 88, 67–69.
• Rao, C. R. (1993) "Is Pitman Closeness a Reasonable Criterion?: Comment", Journal of the American Statistical Association, 88, 69–70.