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Pitman closeness criterion

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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

  • Pitman, E. (1937) "The “closest” estimates of statistical parameters". Mathematical Proceedings of the Cambridge Philosophical Society, 33 (2), 212–222. doi:10.1017/S0305004100019563
  • 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. doi:10.1016/0378-3758(90)90046-W
  • 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, 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.
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