On Comparisons between Confidence Point Procedures in the Case of a Single Parameter
作者： B. L. Welch
DOI: 10.1111/J.2517-6161.1965.TB00580.X
关键词:
摘要: SUMMARY In a recent paper (Welch and Peers, 1963) formulae were obtained for confidence points depending on the distributional properties of certain integrals weighted likelihoods. Some comparisons are made here with SUPPOSE sample S has probability element p(S, 0) dS = exp {L(S, 0)} dS. We concerned in main situations where L(S, is "in sense" 0(n), n can become large. For "almost all samples" there then single maximumlikelihood estimate T which will differ from 0 by 0(n-A). write K2(0) E{(n-iaL/a6)2} _E(n-E 32L/62), (1) but convenience we shall often abbreviate K2(T) to K2 K2(6) simply K2. Asymptotically ni K'(T- tends be distributed normally mean zero standard deviation unity. The quantity iK2(6 - T) also have same distribution. More precisely Pr{n K2(6-T) < x} 0s+0(n-), (2) e cx related
jstor.org 
sci-hub.se 参考文章(10)
A. R. Thatcher, Relationships between Bayesian and Confidence Limits for Predictions Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 26, pp. 176- 192 ,(1964) , 10.1111/J.2517-6161.1964.TB00551.X
E. A. Cornish, R. A. Fisher, 148: Moments and Cumulants in the Specification of Distributions. Revue de l'Institut International de Statistique / Review of the International Statistical Institute. ,vol. 5, pp. 307- ,(1938) , 10.2307/1400905
Harold Jeffreys, An invariant form for the prior probability in estimation problems. Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 186, pp. 453- 461 ,(1946) , 10.1098/RSPA.1946.0056
M. S. BARTLETT, APPROXIMATE CONFIDENCE INTERVALS Biometrika. ,vol. 40, pp. 12- 19 ,(1953) , 10.1093/BIOMET/40.1-2.12
Two New Properties of Mathematical Likelihood Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 144, pp. 285- 307 ,(1934) , 10.1098/RSPA.1934.0050
B. L. WELCH, ON THE DISTRIBUTION OF MAXIMUM LIKELIHOOD ESTIMATES Biometrika. ,vol. 31, pp. 187- 190 ,(1939) , 10.1093/BIOMET/31.1-2.187
B. L. Welch, H. W. Peers, On Formulae for Confidence Points Based on Integrals of Weighted Likelihoods Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 25, pp. 318- 329 ,(1963) , 10.1111/J.2517-6161.1963.TB00512.X
J. Aitchison, Two Papers on the Comparison of Bayesian and Frequentist Approaches to Statistical Problems of Prediction: Bayesian Tolerance Regions Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 26, pp. 161- 175 ,(1964) , 10.1111/J.2517-6161.1964.TB00550.X
D. V. Lindley, Fiducial Distributions and Bayes' Theorem Journal of the royal statistical society series b-methodological. ,vol. 20, pp. 102- 107 ,(1958) , 10.1111/J.2517-6161.1958.TB00278.X
D. A. S. Fraser, On the Consistency of the Fiducial Method Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 24, pp. 425- 434 ,(1962) , 10.1111/J.2517-6161.1962.TB00469.X