In statistical theory, the Pitman closeness criterion, named after

E. J. G. Pitman Edwin James George Pitman (29 October 1897 – 21 July 1993) was an Australian mathematician who made significant contributions to statistics and probability theory. In particular, he is remembered primarily as the originator of the Pitman per ...

, 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 The Mahalanobis distance is a measure of the distance between a point ''P'' and a distribution ''D'', introduced by P. C. Mahalanobis in 1936. Mahalanobis's definition was prompted by the problem of identifying the similarities of skulls based ...

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. *Rukhin, A. (1996) "On the Pitman closeness criterion from the decision – Theoretic point of view". ''Statistics & Decisions'', 14, 253–274. *Peddada, D. S. (1985) "A short note on Pitman’s measure of nearness". ''American Statistician'', 39, 298–299. *Peddada, D. S. (1986) "Reply". ''American Statistician'', 40, 2576 *Nayak, T. K. (1990) "Estimation of location and scale parameters using generalized Pitman nearness criterion". ''Journal of Statistical Planning and Inference'', 24, 259–268. *Nayak, T. K. (1994) "Pitman nearness comparison of some estimators of population variance", ''American Statistician'' 48, 99–102. *Nayak, T. K. (1998) "On equivariant estimation of the location of elliptical distributions under Pitman closeness criterion", ''Statistics and Probability Letters'' 36, 373–378. *Fountain, R. L. (1991) "Pitman closeness comparison of linear estimators: A canonical form", ''Commun. Statist.–Theory Meth.'', 20 (11), 3535–3550. *Ghosh, M.; Sen, P. K. (1989) ''Median unbiasedness and Pitman closeness''. '' Journal of the American Statistical Association'', 84, 1089–1091. *Johnson, N. L. (1950) "On the comparison of estimators", ''

Biometrika ''Biometrika'' is a peer-reviewed scientific journal published by Oxford University Press for thBiometrika Trust The editor-in-chief is Paul Fearnhead (Lancaster University). The principal focus of this journal is theoretical statistics. It was es ...

'', 37, 281–287. *Keating, J. P.; Gupta, R. C. (1984) "Simultaneous comparison of scale estimators". '' Sankhya'', Ser. B 46, 275–280. *Keating, J. P.; Mason, R. L.; Sen, P. K. (1993) ''Pitman’s Measure of Closeness: A Comparison of Statistical Estimators'', SIAM, Philadelphia. *Kubokawa, T. (1991) "Equivariant estimation under the Pitman closeness criterion". ''Commun. Statist.–Theory Meth.'', 20 (11), 3499–3523. *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. Statistical distance Point estimation performance