论文检索

统计决策理论导论AI 解读

The Bayesian revolution in statistics -- where statistics is integrated with decision making in areas such as management, public policy, engineering, and clinical medicine -- is here to stay. Introduction to Statistical Decision Theory states the case and in a self-contained, comprehensive way shows how the approach is operational and relevant for real-world decision making under uncertainty. Starting with an extensive account of the foundations of decision theory, the…

摘要暂缺

代理变量对回归系数影响的界限AI 解读

We consider a regression in which one of the observed variables is a proxy for some unobserved variable. Given a lower bound for the correlation between the proxy and the unobserved true variable for which it substitutes, we derive intervals in which the coefficients of the unobserved true regression must lie, regardless of any other correlations involving unobserved variables or disturbances. We present a simple solution for the important special case in which only the…

对数似然的凹性AI 解读

For a very general regression model with an ordinal dependent variable, the log likelihood is proved concave if the derivative of the underlying response function has concave logarithm. For a binary dependent variable, a weaker condition suffices, namely, that the response function and its complement each have concave logarithm. The normal, logistic, sine, and extreme-value distributions, among others, satisfy the stronger condition, the t (including Cauchy) distributions…

Edgeworth 与 Fisher 关于最大似然估计效率的研究AI 解读

F. Y. Edgeworth's 1908-9 investigation is examined for its contribution to knowledge of the sampling properties of maximum likelihood and related estimates, especially asymptotic efficiency. The nature and extent of his progress and anticipation of R. A. Fisher are described. Fisher's relevant work is briefly examined in relation to Edgeworth's and to the Cramer-Rao inequality.

二项、F、Beta 及相关尾概率的正态近似（二）AI 解读

This paper describes and derives the asymptotic behavior of the new Normal approximation introduced in Part I and of a family of Normal approximations based on roots, including the square root approximations of Fisher, and Freeman and Tukey, and the cube root approximations of Wilson and Hilferty, Camp, and Paulson. Various asymptotic comparisons are made, all of which rank the new approximation first, the cube root approximations second, and the other root approximations…

一阶平稳马尔可夫残差下样本均值的效率AI 解读

The efficiency of the sample mean relative to the “best” linear unbiased estimator when residuals follow a first-order stationary Markoff process is studied. The minimum efficiency for correlation ρ ≧ 0 occurs at the unique root of a certain equation depending on the sample size n and decreases monotonically in n toward the value .878 obtained by Ylvisaker in the continuous case. It is tabulated for selected n ≦ 300, together with the value of p at which the minimum is…

二项、F、贝塔及其他相关常见分布尾概率的正态近似（一）AI 解读

This paper concerns a new Normal approximation to the beta distribution and its relatives, in particular, the binomial, Pascal, negative binomial, F, t, Poisson, gamma, and chi square distributions. The approximate Normal deviates are expressible in terms of algebraic functions and logarithms, but for desk calculation it is preferable in most cases to use an equivalent expression in terms of a function specially tabulated here. Graphs of the error are provided. They show…

摘要暂缺

摘要暂缺

摘要暂缺

置信区间的长度AI 解读

The expected length of a confidence interval is shown to equal the integral over false values of the probability each false value is included. Thus two desiderata for choosing among confidence procedures lead to the same measure of desirability. Furthermore, by common definitions of “optimum,” a procedure is optimum as regards including false values if and only if it is optimum as regards expected length. However, the procedure with minimum expected length ordinarily depends…

Wilcoxon符号秩程序中零值与并列值的讨论AI 解读

A Wilcoxon one-sample signed rank test may be made when some of the observations are 0 by dropping the 0's before ranking. However, a sample can be not significantly positive while a more negative sample (obtained by decreasing each observation equally), is significantly positive by the ordinary Wilcoxon test. The reverse is also possible. Two-piece confidence regions result. A procedure for avoiding these difficulties is proposed, namely to rank the observations including…