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大样本中的有效估计与最优推断程序AI 解读

SUMMARY The concept of efficiency in estimation is linked with closeness of approximation to the derivative of log likelihood, which plays an important role in statistical inference in large samples. Various orders of efficiency are defined depending on degrees of closeness, and properties of estimates satisfying these criteria are studied. Such measures of efficiency appear to be more appropriate than the one related to asymptotic variance of an estimate for judging the…

广义幂级数分布的最大似然估计及其在截断二项分布中的应用AI 解读

G. P. PATIL; Maximum likelihood estimation for generalized power series distributions and its application to a truncated binomial distribution, Biometrika, Volu

变量相依时的有效矩估计：以第二类删失正态数据为例AI 解读

pair of equations in ,u and &, the maximum likelihood estimates of ,u and o, are tiresome to handle computationally (Gupta, 1952). Though some considerable attention has been given to the solution of the maximum likelihood equations in this case (Cohen, 1957), and various alternatives to the maximum likelihood estimators have been proposed (Sarhan & Greenberg, 1956, 1958; Saw, 1959), it remains an interesting field in which to apply the methods suggested in this paper.…

截断二项与负二项分布参数矩估计的渐近方差AI 解读

In this paper the asymptotic variances of method of moments estimates of the parameters of the truncated binomial and negative binomial distributions have been derived. For the binomial distribution with one class from the lower end of the distribution truncated, the efficiency of the estimate relative to maximum likelihood has been compared.

比较两个总体中二元特征的关联强度AI 解读

Asymptotically favorable methods for testing the equality of certain measures of association in different four-fold tables are deduced from the general theory of χ2-tests as given by Neyman and generalized by Anderson, Goodman and Gold. The tests turn out to be also obtainable by an intuitive use of maximum likelihood estimates as suggested by Wald's large sample theory and include one proposed by Lancaster for testing the second order interaction in a complex contingency…

比较两个总体中二元特征的关联强度AI 解读

Asymptotically favorable methods for testing the equality of certain measures of association in different four-fold tables are deduced from the general theory of χ2-tests as given by Neyman and generalized by Anderson, Goodman and Gold. The tests turn out to be also obtainable by an intuitive use of maximum likelihood estimates as suggested by Wald's large sample theory and include one proposed by Lancaster for testing the second order interaction in a complex contingency…

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非线性系统的可识别性判据AI 解读

This paper considers the problem of criteria for the identifiability of a structural equation which is one of a set of equations linear in the parameters but not in the variables. The criteria are developed in terms of parameter restrictions of the rank condition type. By expansion in Taylor's series and combination with the results of Fisher [2], these results can be easily extended to far more general nonlinear systems. THE USUAL treatment of identifiability criteria is…

截断分组双曲正割平方分布的位置与尺度参数估计AI 解读

The iterative calculations required to obtain the maximum likelihood estimates of α and β in the distribution function dF(z) = e z /(1 + e z )2 dz, where z = α +βx, are presented for doubly truncated, upper and lower truncated, and untruncated grouped samples. The calculations needed to obtain the maximum likelihood estimator of Pareto's constant are also given for a lower truncated grouped sample with both equal and unequal grouping. Asymptotic variances and covariances are…

方差下界的另一面：一则附有更正的札记AI 解读

This note has as its primary purpose the correction of a statement made in a previous paper regarding the attainment of the variance of a proposed estimator of its lower bound. At the same time it seemed useful, as an expository function, to recapitulate a development of the lower bound which led this writer to a better understanding of it, and to the realization of the indicated error. Here the bound is developed ab initio from a simple identity, instead of secondarily from…

方差下界的另一面：一则更正札记AI 解读

This note has as its primary purpose the correction of a statement made in a previous paper regarding the attainment of the variance of a proposed estimator of its lower bound. At the same time it seemed useful, as an expository function, to recapitulate a development of the lower bound which led this writer to a better understanding of it, and to the realization of the indicated error. Here the bound is developed ab initio from a simple identity, instead of secondarily from…

一种最大似然估计方法AI 解读

SUMMARY Knowledge of one or more of the parameters in a maximum-likelihood problem sometimes results in a very considerable simplification, the analysis becoming almost trivial. A method of obtaining maximum-likelihood estimates and their asymptotic covariance matrix is given which makes it possible to capitalize on simplifications of this sort when they arise. Application is mainly in the field of regression, but other examples are mentioned. A numerical example of…

相依随机变量情形下最大似然法的一则说明AI 解读

SUMMARY The validity of certain statistical procedures depends on the “classical” properties of the method of maximum-likelihood, viz., its consistency and the fact that it leads to an estimator whose asymptotic variance can be derived easily from the likelihood function. These properties are well established for the case where successive observations are independent. Here it is shown that their extension to the dependent case involves suitable behaviour of two…

分布滞后的估计：评论AI 解读

Considering first the case of a known autocorrelation coefficient $, Klein observes that (4) may be viewed as a structural linear relation between the latent variables yt' -et, xI and yt'-l -et-,. Even knowing $, two of those variables are not observable. But the y' and yt' may be computed; et and et-, may be considered as errors of observation of the corresponding latent variables. In comparison with the classical models containing errors in variables, (4) is somewhat…

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泊松过程的多元回归分析AI 解读

A multiple regression model based on the Poisson density is discussed. Point estimation by maximum likelihood results in estimating equations which can be solved by iteration based on scoring or on a successively revised weighted least squares estimator. The first round of each iterative process is shown to be BAN, provided that the ordinary least squares estimator is used as the initial condition. A minimum chi-squared estimator, which can be computed directly from sample…

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Ⅱ型删失正态样本中位置与尺度参数极大似然估计的偏差AI 解读

J. G. SAW; The bias of the maximum likelihood estimates of the location and scale parameters given a type II censored normal sample, Biometrika, Volume 48, Issu

截断与删失样本下多元正态总体参数的估计AI 解读

SUMMARY This paper is concerned with the problem of estimation of means and variances of a k-variate normal distribution from a sample doubly truncated or censored on s-variates (s ≤ k), when variates are uncorrelated. Maximum likelihood equations are derived which, with the help of normal probability tables, can readily be solved by iteration. The information matrix is given from which the asymptotic variances and covariances of the estimates can be determined. to…

不同联立方程估计量的蒙特卡洛研究AI 解读

We study the small sample properties of the simultaneous equation estimators by a Monte Carlo approach. The four methods of estimation considered are: least squares, two-stage least squares, unbiased and minimumsecond-moment. The last of these four methods possesses the smallest secondorder sampling moments about the true parameter value in a majority of cases, while two-stage least squares shows the smallest bias in all cases. It is also founld that the usual asymptotic…

零值截断且部分单次计数缺失时的泊松分布估计AI 解读

This paper is concerned with maximum likelihood estimation of the Poisson parameter λ when the zero class has been truncated and when errors of observation have resulted in eliminating some though not necessarily all of the one class. Estimators are derived both for λ and the proportion θ of ones eliminated as a consequence of faulty observation. A table and a graph of the estimation function involved are given. Asymptotic variances and covariances of the estimators are…