mathematics

Pitman closeness criterion

Pitman closeness criterion is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Pitman closeness criterion rather than just read about it. In short: In statistical theory, the Pitman closeness criterion, named after E. J.

Key takeaways

Pitman closeness criterion belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Pitman closeness criterion to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Pitman closeness criterion from memory before moving on to harder problems.

Reference excerpt

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.

Worked examples

Example 1 — a first encounter with Pitman closeness criterion

Start with the simplest possible case. Write down what Pitman closeness criterion claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Pitman closeness criterion before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Pitman closeness criterion ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Pitman closeness criterion

In research: Pitman closeness criterion appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Pitman closeness criterion in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Pitman closeness criterion is common in secondary-school and first-year university syllabi. It links to neighbouring topics Point estimation performance, Statistical distance, so understanding it makes those chapters shorter.
In everyday life: Look for Pitman closeness criterion outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Pitman closeness criterion in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Pitman closeness criterion means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Pitman closeness criterion out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Pitman closeness criterion in simple terms?

In statistical theory, the Pitman closeness criterion, named after E. J.

Why does Pitman closeness criterion matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Pitman closeness criterion?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Pitman closeness criterion.