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多参数情形下最大似然迭代程序的收敛问题AI 解读

In multiparameter situations there are important problems of convergence in the solution of maximum likelihood iterative equations. Convergence may be critically dependent on the initial parameter estimates employed. These problems are indicated specifically for a model of exponentially-distributed lifetimes where the reciprocal of the exponential parameter is linearly dependent on various regressor variables. A strategy is suggested based on alternative use of observed or…

缺失数据下多元正态参数极大似然估计的期望与方差AI 解读

Exact expectations and variances have been obtained for the maximum likelihood estimates of the elements of the mean vector and covariance matrix of the multivariate normal distribution when a subset of the variates does not have observations on some sampling units. The biases, variances, and mean square errors of the estimates are compared with those of the usual estimates computed from the complete observation vectors. When the correlations between the complete and…

多参数情形下最大似然迭代程序的收敛问题AI 解读

In multiparameter situations there are important problems of convergence in the solution of maximum likelihood iterative equations. Convergence may be critically dependent on the initial parameter estimates employed. These problems are indicated specifically for a model of exponentially-distributed lifetimes where the reciprocal of the exponential parameter is linearly dependent on various regressor variables. A strategy is suggested based on alternative use of observed or…

扰动较小时 k 类估计量的比较AI 解读

A new approach to the choice of econometric estimators, called small-sigma asymptotics, is introduced and applied to the choice of k-class estimators of the parameters of a single equation in a system of linear simultaneous stochastic equations. I find that when the degree of overidentification is no more than six, the two stage least squares estimator uniformly dominates the limited information maximum likelihood estimator in a certain sense. The small sigma method can be…

对 Choi 与 Bulgren《分布混合的估计程序》的评论AI 解读

Summary Choi and Bulgren's (1968) estimator for the mixing measure of a mixture of known distributions is biased in small samples; a variant of their estimator has a much smaller bias, and a smaller mean squared error, for mixtures of normal distributions differing in mean. The maximum-likelihood estimator is shown to be more computable than Choi and Bulgren suggest. Estimation is much more difficult when the component distributions are unknown; for example, a mixture of two…

若干非标准情形下最大似然估计量的渐近性质AI 解读

Most results on the asymptotic properties of maximum likelihood estimators are for the standard cases where we observe independent and identically distributed random variables, whose distribution satisfies certain regularity conditions. In this article, similar properties are shown to hold for a class of cases where the observed random variables are not necessarily independent and identically distributed.

事故发生率潜势：泊松过程多元回归分析的应用AI 解读

Various accident frequency models have appeared in the literature which predict the distribution of future accidents based on the number of past accidents. This article presents a method for deriving such distributions using several predictive criteria. It is assumed that an individual's accident experience is a Poisson process with the parameter a linear function of criterion variables. An iterative weighted least-squares procedure is used to solve the system of maximum…

分组泊松数据的极大似然估计AI 解读

In this article, sufficient conditions are given for the existence of a unique solution of the likelihood equation which results from a grouped data sample. The necessary and sufficient conditions for the convergence of a sequence defined by the method of successive approximations to this unique solution are also given. Finally, it is shown that when the groups from an underlying Poisson distribution are connected the method of successive approximations will converge to the…

分组 Poisson 数据的极大似然估计AI 解读

In this article, sufficient conditions are given for the existence of a unique solution of the likelihood equation which results from a grouped data sample. The necessary and sufficient conditions for the convergence of a sequence defined by the method of successive approximations to this unique solution are also given. Finally, it is shown that when the groups from an underlying Poisson distribution are connected the method of successive approximations will converge to the…

事故发生率潜势：泊松过程的多元回归分析AI 解读

Various accident frequency models have appeared in the literature which predict the distribution of future accidents based on the number of past accidents. This article presents a method for deriving such distributions using several predictive criteria. It is assumed that an individual's accident experience is a Poisson process with the parameter a linear function of criterion variables. An iterative weighted least-squares procedure is used to solve the system of maximum…

最优线性估计量的经验贝叶斯版本及二项分布应用AI 解读

An empirical Bayes estimator is one which estimates the posterior mean by making use of past data. For certain conditional distributions though, no empirical Bayes estimator can be found which converges to the posterior mean as past data are accumulated. However, an optimal linear estimator for a parameter, say θ1 can often be found. This optimal linear estimator depends upon the first two prior moments, both of which can often be estimated. The resulting estimator has been…

最小二乘回归中的序列相关检验（三）AI 解读

The paper considers a number of problems arising from the test of serial correlation based on the d statistic proposed earlier by the authors (Durbin & Watson, 1950, 1951). Methods of computing the exact distribution of d are investigated and the exact distribution is compared with six approximations to it for four sets of published data. It is found that approximations suggested by Theil and Nagar and by Hannan are too inaccurate for practical use but that the beta…

向固定点收缩的均值估计AI 解读

The problem of shrinking the maximum likelihood estimator (MLE) of the mean μ of various populations towards a natural origin μ0 is studied. Estimators of the general form, are proposed for the cases of Normal, Gamma, Poisson, and Binomial distributions. The behavior of these estimators is compared with that of the ones suggested by Thompson [3]. Our estimators are shown to be better in the sense of having a smaller mean square error in an interval around μ0.

不完整多项分布数据的极大似然估计AI 解读

When sampling from a multinomial population, it may happen either by chance or by design that some of the observations are only partially classified. In this article the amount of information in the partially classified observation is evaluated, and maximum likelihood estimators are obtained using both completely classified and partially classified data. In general an iterative solution is required, but special cases are identified in which the solution is obtained in closed…

合并横截面与时间序列数据中的方差分量模型AI 解读

The paper argues that variance components models are very useful in pooling cross section and time series data because they enable us to extract some information about the regression parameters from the between group and between time-period variation-a source that is often completely eliminated in the commonly used dummy variable techniques. The paper studies the applicability and usefulness of the maximum likelihood method and analysis of covariance techniques in the…

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依赖观测下最大似然估计的渐近性质AI 解读

Summary The problem of weak consistency and asymptotic efficiency of the maximum-likelihood estimate in the case of dependent random variables (observations) is considered. A set of readily applicable conditions that ensure these properties of the maximum-likelihood estimate is presented. The conditions are expressed in terms of the probability density distribution of individual observations, conditioned upon all past observations. The connection between these conditions and…

报告率恒定时利用鸟环回收估计年龄别存活率AI 解读

A probability model consisting of a product of multinomial distributions is derived for a bird-banding experiment in which a new batch of nestlings is banded and released at the beginning of each year and the bands from the dead birds are returned by observers in subsequent years. The annual reporting probability is assumed to be the same for all birds and to remain constant from year to year, while the probability of survival is assumed to depend on the age of the bird…

区组大小不等时的区组间信息恢复AI 解读

A method is proposed for estimating intra-block and inter-blook weights in the analysis of incomplete block designs with block sizes not necessarily equal. The method consists of maximizing the likelihood, not of all the data, but of a set of selected error contrasts. When block sizes are equal results are identical with those obtained by the method of Nelder (1968) for generally balanced designs. Although mainly concerned with incomplete block designs the paper also gives…

最优线性估计量的经验贝叶斯版本及其二项分布应用AI 解读

An empirical Bayes estimator is one which estimates the posterior mean by making use of past data. For certain conditional distributions though, no empirical Bayes estimator can be found which converges to the posterior mean as past data are accumulated. However, an optimal linear estimator for a parameter, say θ1 can often be found. This optimal linear estimator depends upon the first two prior moments, both of which can often be estimated. The resulting estimator has been…

最小二乘回归中的序列相关检验：第三篇AI 解读

The paper considers a number of problems arising from the test of serial correlation based on the d statistic proposed earlier by the authors (Durbin & Watson, 1950, 1951). Methods of computing the exact distribution of d are investigated and the exact distribution is compared with six approximations to it for four sets of published data. It is found that approximations suggested by Theil and Nagar and by Hannan are too inaccurate for practical use but that the beta…

不完整列联表中的准独立性与最大似然估计AI 解读

Many authors have been concerned with contingency tables containing cells which are missing, a priori zero or otherwise specified. This article examines the problem of maximum likelihood estimation for such tables under the “quasi-in-dependence” model. In particular, conditions are provided to ensure the existence of unique nonzero maximum likelihood estimates for the cells of incomplete tables obtained by deleting the missing or a priori zero cells, even when other cells…

列联表交互作用检验：最小 Logit 卡方估计与最大似然估计的比较AI 解读

This article compares small sample properties of 12 goodness of fit tests for interaction in 2×2×2 and 3×2×2 contingency tables. The 12 tests are constructed by-combining three tests (the minimum logit chi-square test, the Pearson chi-square test, and the likelihood ratio test) and four methods of estimation (the iterative maximum likelihood estimator and three variants of the non-iterative minimum logit chi-square estimator). An evaluation is made of the adequacy of the…

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