XV.—On the Estimation of Statistical Parameters

Aitken, A. C.; Silverstone, H.

doi:10.1017/s008045410000618x

Cited by 28 publications

(22 citation statements)

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“…While the Cram Â er-Rao bound (see equation 2.8) provides a general lower bound on the c.m.s.e. of any estimator (Aitken & Silverstone, 1942;Frechet, 1943;Rao, 1946;Cram Â er, 1946), this inequality does not justify the use of Fisher information as a general measure for the precision of population codes, because the Cram Â er-Rao bound is not unique for biased estimators, and it often cannot be attained. Furthermore, the notion of an ideal observer is not unique, so that no general denition of the resolution exists that ts all problems, but any denition necessarily depends on further specications.…”

Section: Introductionmentioning

confidence: 99%

Optimal Short-Term Population Coding: When Fisher Information Fails

2002

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Efcient coding has been proposed as a rst principle explaining neuronal response properties in the central nervous system. The shape of optimal codes, however, strongly depends on the natural limitations of the particular physical system. Here we investigate how optimal neuronal encoding strategies are inuenced by the nite number of neurons N (place constraint), the limited decoding time window length T (time constraint), the maximum neuronal ring rate f max (power constraint), and the maximal average rate h f i max (energy constraint). While Fisher information provides a general lower bound for the mean squared error of unbiased signal reconstruction, its use to characterize the coding precision is limited. Analyzing simple examples, we illustrate some typical pitfalls and thereby show that Fisher information provides a valid measure for the precision of a code only if the dynamic range ( f min T, f max T) is sufciently large. In particular, we demonstrate that the optimal width of gaussian tuning curves depends on the available decoding time T. Within the broader class of unimodal tuning functions, it turns out that the shape of a Fisher-optimal coding scheme is not unique. We solve this ambiguity by taking the minimum mean square error into account, which leads to at tuning curves. The tuning width, however, remains to be determined by energy constraints rather than by the principle of efcient coding.

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Section: Introductionmentioning

confidence: 99%

Optimal Short-Term Population Coding: When Fisher Information Fails

2002

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“…Campbell) to return to work in New Zealand, a respected teacher and researcher and a controversial figure because of his political views. This paper extends Roberts's contribution by expanding the account of Silverstone's mathematical work, especially the paper by Aitken & Silverstone (1941), which grew out of Silverstone's PhD thesis. That paper was important in its own right as a major step in the elucidation of the properties of minimum variance estimates, and as a precursor to the discovery of the Cramér-Rao lower bound.…”

Section: Introductionmentioning

confidence: 62%

“…Although this work was done under considerable difficulties -he was severely ill with nephritis during part of it -the thesis developed some key results in estimation theory. These were published subsequently in the famous paper by Aitken & Silverstone (1941). The thesis itself (Silverstone, 1939) has also been referenced extensively.…”

Section: Biographical Sketchmentioning

confidence: 99%

“…As Aitken and Silverstone remarked in their introduction (Aitken & Silverstone, 1941), their starting point was . .…”

Section: The Minimum Variance Papermentioning

confidence: 99%

“…It has been suggested by some writers, such as Kendall & Stuart (1967), that Aitken & Silverstone (1941) contains the essentials of the Cramér-Rao lower bound, which first appeared in explicit published form in the papers by Rao (1945) and Cramér (1946). Indeed, it is trivially true that the Aitken-Silverstone paper implies that, when an exact minimum variance unbiased estimate exists, the variance of any other estimate for the same quantity must exceed the Cramér-Rao lower bound.…”

Section: The Minimum Variance Papermentioning

confidence: 99%

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Applications: Harold Silverstone: A Perspective

Vere-Jones

Mackinnon

Silverstone

2001

Aus NZ J of Statistics

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This paper is a perspective on the scientific contributions of the politically controversial New Zealand-born statistician Harold Silverstone . His scientific work -including a classic paper on minimum variance with A.C. Aitken -produced some key results in estimation theory. He also contributed significantly to the practical application of statistics, particularly the development of statistical consulting services in medicine.

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Minimum Variance Unbiased ( MVU ) Estimator

Bethel

2005

Encyclopedia of Biostatistics

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Determining the minimum variance of an unbiased estimator constitutes a fundamental topic in mathematical statistics. Two primary results are the Cramér–Rao inequality, which gives a lower bound on the variance of an unbiased estimator, and the Rao–Blackwell theorem, which supplies a method for improving the variance of unbiased estimators that are not functions of sufficient statistics. The strongest results are available for sufficient statistics from complete exponential families. However, any functions of sufficient statistics will attain the Cramér–Rao lower bound for sufficiently large sample sizes.

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XV.—On the Estimation of Statistical Parameters

Cited by 28 publications

References 1 publication

Optimal Short-Term Population Coding: When Fisher Information Fails

Optimal Short-Term Population Coding: When Fisher Information Fails

Applications: Harold Silverstone: A Perspective

Minimum Variance Unbiased ( MVU ) Estimator

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