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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
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- 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
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- Rao, C. R. (1993) "Is Pitman Closeness a Reasonable Criterion?: Comment", Journal of the American Statistical Association, 88, 69–70.