Abstract
THE current mathemetical theories concerned with the estimation of one or more unknown parameters in a frequency distribution have been the occasion of much controversy, and the absence of a systematic review of this field at a sufficiently elementary level has been a serious obstacle to the student. Two recent articles by Dr. Leon Solomon published in the Journal of the Institute of Actuaries Students9 Society (7, 144 and 213) go a long way towards meeting this need, and form a most welcome addition to the literature. The first article is chiefly concerned with 'point' estimation. The concept of sufficiency is discussed, the minimum-variance theorem is proved, and the method of maximum likelihood is introduced, the proofs of its main properties being given in outline. The second article is concerned with 'interval' estimation, first from the point of view of the theory of confidence intervals and then in terms of fiducial probability, the contrast between these two methods of approach being illustrated by a discussion of the Behrens–Fisher problem. Rigorous proofs of the theorems are not attempted, and the emphasis throughout is laid on the new ideas which are involved. Another welcome feature of the presentation is the inclusion of many worked examples.
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Statistical Estimation. Nature 163, 356–357 (1949). https://doi.org/10.1038/163356d0
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DOI: https://doi.org/10.1038/163356d0