# On the Mathematical Foundations of Theoretical Statistics

@article{FisherOnTM, title={On the Mathematical Foundations of Theoretical Statistics}, author={Rory A. Fisher}, journal={Philosophical Transactions of the Royal Society A}, volume={222}, pages={309-368} }

Centre of Location. That abscissa of a frequency curve for which the sampling errors of optimum location are uncorrelated with those of optimum scaling. (9.)

## 3,160 Citations

Probabilistic estimation of poles or zeros of functions

- Mathematics
- 1979

Abstract A Maximum Likelihood method is presented for the purpose of estimating the positions of poles or zeros of certain classes of functions of a complex variable from information on ordinate…

Probability Limits, Asymptotic Distributions, and Properties of Maximum Likelihood Estimators

- Mathematics
- 1974

The purpose of this chapter is to introduce certain basic results from probability and statistical theory. A thorough understanding of such results is quite essential to those wishing a complete…

On Statistics Independent of Sufficient Statistics

- Mathematics
- 2011

In an earlier paper (1955) the author stated that any statistic independent of a sufficient statistic must have the same distribution for all values of the unknown parameter. An example is given here…

Asymptotic Optimality of Estimators

- Mathematics
- 2017

Nonasymptotic theory, which flourished between 1940 and 1960, ended up as a collection of results that does not amount to a consistent theory.

XV.—On the Estimation of Statistical Parameters

- Mathematics
- 1942

In the problem of estimating from sample the value of a parameter in a probability function new postulates are suggested of unbiased linear estimate and minimum sampling variance. A comparison is…

Implications of Informational Point of View on the Development of Statistical Science

- Computer Science
- 1994

Informational approach represents a new trend in the development of statistical science. This paper is intended for the discussion of the informational outlook in relation to the development of…

R. A. Fisher on the Design of Experiments and Statistical Estimation

- Computer Science
- 1992

The purpose in this talk is to consider the relation between two of Fisher’s major contributions: his theory of experimental design and the theory of statistical estimation.

Mathematical Foundations of Infinite-Dimensional Statistical Models

- Mathematics
- 2015

1. Nonparametric statistical models 2. Gaussian processes 3. Empirical processes 4. Function spaces and approximation theory 5. Linear nonparametric estimators 6. The minimax paradigm 7.…

Some pioneers of modern statistical theory: a personal reflection

- Mathematics
- 2016

An outline account is given of the work of nine major figures working mostly in the earlier two-thirds of the 20th century. Some comments are included about their personal characteristics.

Minimaxity, More or Less

- Mathematics
- 1994

This is a historical study of the minimax idea in statistics and of its creator, Abraham Wald. The focus is on the place of minimaxity in the development of statistics over the last half century.

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Any experiment may be regarded as forming an individual of a “population” of experiments which might be performed under the same conditions. A series of experiments is a sample drawn from this…

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(1) Introductory.—In a memoir recently presented to the Royal Society, I have endeavoured to emphasise the importance of distinguishing between three diverse types of heredity, namely (i), Blended…

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Let x1, x2 … x n be a system of deviations from the means of n variables with standard deviations σ1, σ2 … σ n and with correlations r12, r13, r23 … r n −1,n.

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1. If we set ourselves the problem, in its essence one of frequent occurrence, of finding the arbitrary elements in a function of known form, which best suit a set of actual observations we are met…

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by the method of moments. This method of moments has been extended by Thiele, Pearson, Lapps and others to obtain the constants involved in various stew frequency curves and series. It is an…

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An erratum slip is printed and can be obtained by purchasers of the above series by sending a stamped and addressed envelope to Mr. C. F. Clay, Cambridge University Press, Fetter Lane, E.G.C.