Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 871
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Akahira, M. and Ohyauchi, N. 2016. Second order asymptotic loss of the MLE of a truncation parameter for a truncated exponential family of distributions. Communications in Statistics - Theory and Methods,

    Alipour, Mojtaba and Safari, Zahra 2016. From information theory to quantitative description of steric effects. Phys. Chem. Chem. Phys., Vol. 18, Issue. 27, p. 17917.

    Balasis, Georgios Potirakis, Stelios M. and Mandea, Mioara 2016. Investigating Dynamical Complexity of Geomagnetic Jerks Using Various Entropy Measures. Frontiers in Earth Science, Vol. 4,

    Bates, B. T. Dufek, J. S. James, C. R. Harry, J. R. and Eggleston, J. D. 2016. The Influence of Experimental Design on the Detection of Performance Differences. Measurement in Physical Education and Exercise Science, p. 1.

    Berrada, K 2016. Trapping phenomenon of the parameter estimation in asymptotic quantum states. Laser Physics, Vol. 26, Issue. 9, p. 095203.

    Cai, Li Choi, Kilchan Hansen, Mark and Harrell, Lauren 2016. Item Response Theory. Annual Review of Statistics and Its Application, Vol. 3, Issue. 1, p. 297.

    Clarkson, Eric and Cushing, Johnathan B. 2016. Shannon information for joint estimation/detection tasks and complex imaging systems. Journal of the Optical Society of America A, Vol. 33, Issue. 3, p. 286.

    Clarkson, Eric and Cushing, Johnathan B. 2016. Shannon information and receiver operating characteristic analysis for multiclass classification in imaging. Journal of the Optical Society of America A, Vol. 33, Issue. 5, p. 930.

    Desmond, Anthony F. 2016. Wiley StatsRef: Statistics Reference Online.

    Falaye, B.J. Serrano, F.A. and Dong, Shi-Hai 2016. Fisher information for the position-dependent mass Schrödinger system. Physics Letters A, Vol. 380, Issue. 1-2, p. 267.

    Hall, Michael J. W. and Reginatto, Marcel 2016. Ensembles on Configuration Space.

    He, Juan Ding, Zhi-Yong and Ye, Liu 2016. Enhancing quantum Fisher information by utilizing uncollapsing measurements. Physica A: Statistical Mechanics and its Applications, Vol. 457, p. 598.

    Hero, Alfred O. and Rajaratnam, Bala 2016. Foundational Principles for Large-Scale Inference: Illustrations Through Correlation Mining. Proceedings of the IEEE, Vol. 104, Issue. 1, p. 93.

    Jüngel, Ansgar 2016. Entropy Methods for Diffusive Partial Differential Equations.

    Karmali, Faisal Chaudhuri, Shomesh E. Yi, Yongwoo and Merfeld, Daniel M. 2016. Determining thresholds using adaptive procedures and psychometric fits: evaluating efficiency using theory, simulations, and human experiments. Experimental Brain Research, Vol. 234, Issue. 3, p. 773.

    Li, Nan Ferrie, Christopher Gross, Jonathan A. Kalev, Amir and Caves, Carlton M. 2016. Fisher-Symmetric Informationally Complete Measurements for Pure States. Physical Review Letters, Vol. 116, Issue. 18,

    Linke, Yu. Yu. 2016. Refinement of Fisher's One-Step Estimators in the Case of Slowly Converging Initial Estimators. Theory of Probability & Its Applications, Vol. 60, Issue. 1, p. 88.

    Liu, X. M. Cheng, W. W. and Liu, J. -M. 2016. Renormalization-group approach to quantum Fisher information in an XY model with staggered Dzyaloshinskii-Moriya interaction. Scientific Reports, Vol. 6, p. 19359.

    Liu, X. M. Du, Z. Z. and Liu, J.-M. 2016. Quantum Fisher information for periodic and quasiperiodic anisotropic XY chains in a transverse field. Quantum Information Processing, Vol. 15, Issue. 4, p. 1793.

    Liu, Keli and Meng, Xiao-Li 2016. There Is Individualized Treatment. Why Not Individualized Inference?. Annual Review of Statistics and Its Application, Vol. 3, Issue. 1, p. 79.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 22, Issue 5
  • July 1925, pp. 700-725

Theory of Statistical Estimation

  • R. A. Fisher (a1)
  • DOI:
  • Published online: 24 October 2008

It has been pointed out to me that some of the statistical ideas employed in the following investigation have never received a strictly logical definition and analysis. The idea of a frequency curve, for example, evidently implies an infinite hypothetical population distributed in a definite manner; but equally evidently the idea of an infinite hypothetical population requires a more precise logical specification than is contained in that phrase. The same may be said of the intimately connected idea of random sampling. These ideas have grown up in the minds of practical statisticians and lie at the basis especially of recent work; there can be no question of their pragmatic value. It was no part of my original intention to deal with the logical bases of these ideas, but some comments which Dr Burnside has kindly made have convinced me that it may be desirable to set out for criticism the manner in which I believe the logical foundations of these ideas may be established.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

(1)R. A. Fisher (1921). “The mathematical foundations of theoretical statistics.” Phil. Trans. A., vol. 222, pp. 309368.

(2)R. A. Fisher (1920). “A mathematical examination of the methods of determining the accuracy of an observation by the mean error and by the mean square error.’ Monthly Notices of R.A.S. vol. 80, pp. 758770.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *