Method of moments and method of maximum likelihood
成果类型：
Article
署名作者：
Pearson, K
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/28.1-2.34
发表日期：
1936
页码：
3459
关键词：
摘要：
This vigorous paper is a defense of the method of moments for curve fitting as against the claims of R. A. Fisher''s method of maximum likelihood. It is, in large part, a criticism of R. S. Koshal''s Application of the method of maximum likelihood to the improvement of curves fitted by the method of moments (Journ. Roy. Statistical Soc. 96: p.303, 1933). In reply to the statement that Koshal''s paper gave evidence of the superiority of the likelihood method, Pearson says that the argument is invalid since crude moments (without Sheppard''s correction) were used, there was faulty arithmetic, and it was erroneously supposed that the abscissa of the terminal of the frequency curve was the same as the range. Koshal''s paper is held incapable of showing the superiority of maximum likelihood for the further reason that this method was only used to improve an approximation obtained in the first place by the method of moments. Pearson then recomputes the frequency curve corresponding to Koshal''s data by both methods, and finds that by both the [chi]2 and the Likelihood tests, the Method of Moments is superior not inferior to that of Likelihood![long dash]To the memoir are added a note and 2 appendices. The note discusses the assumptions made with regard to the 2 criteria of goodness of fit. Appendix I deals with 3 other papers which discuss that of Koshal. On the whole, I venture to think, these papers tend to confirm the views of my preceding memoir. As a basis for Appendix II, Karl Pearson secured from Bombay some of the original data used by Koshal (they concerned the strength of cotton fibers); with these in hand, he recomputes the frequency curve, and discusses relevant points on curve-fitting.