On the Mathematical Foundations of Theoretical Statistics

  title={On the Mathematical Foundations of Theoretical Statistics},
  author={Rory A. Fisher},
  journal={Philosophical Transactions of the Royal Society A},
  • R. Fisher
  • Mathematics
  • Philosophical Transactions of the Royal Society A
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.) 
Probabilistic estimation of poles or zeros of functions
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
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
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
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
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
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
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
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
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
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.


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
Mathematical contributions to the theory of evolution.—On the law of reversion
  • K. Pearson
  • Economics
    Proceedings of the Royal Society of London
  • 1900
(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
On the Criterion that a Given System of Deviations from the Probable in the Case of a Correlated System of Variables is Such that it Can be Reasonably Supposed to have Arisen from Random Sampling
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.
001: On an Absolute Criterion for Fitting Frequency Curves.
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
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
Mathematical Contributions to the Theory of Evolution. IV. On the Probable Errors of Frequency Constants and on the Influence of Random Selection on Variation and Correlation
(1) In earlier memoirs by one of the present authors, methods have been discussed for the calculation of the constants ( a ) of variation, normal or skew, ( b ) of correla­tion, when normal. The
Tracts for Computers
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.