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最小对比估计量的渐近展开AI 解读

This paper contains an Edgeworth-type expansion for the distribution of a minimum contrast estimator, and expansions suitable for the computation of critical regions of prescribed error (type one) as well as confidence intervals of prescribed confidence coefficient. Furthermore, it is shown that, for one-sided alternatives, the test based on the maximum likelihood estimator as well as the test based on the derivative of the log-likelihood function is uniformly most powerful…

M. H. Pesaran; Exact Maximum Likelihood Estimation of a Regression Equation with a First-Order Moving-Average Error12, The Review of Economic Studies, Volume 40

指数族中两种估计量的渐近等价性AI 解读

It is shown that under certain conditions, the maximum likelihood and the minimum variance unbiased estimators of a positive integral power of the natural parameter in an exponential family have the same asymptotic distribution.

稳定分布抽样下最大似然估计的渐近正态性AI 解读

The large-sample distributions of the maximum-likelihood estimates for the index, skewness, scale, and location parameters (respectively $\alpha, \beta, c$, and $\delta$) of a stable distribution are studied. It is shown that if both $\alpha$ and $\delta$ are unknown, then the likelihood function $L$ will have no maximum within $0 < \alpha \leqq 2, -\infty < \delta < \infty$, but that $L(\alpha, \delta) \rightarrow \infty$ as $(\alpha, \delta) \rightarrow (0, x_k)$ where $x_k$…

截断分布平移参数的最大似然估计AI 解读

$f(x)$ is a uniformly continuous density which equals zero for negative values of $x$, has a right-hand derivative equal to $\alpha$ at $x = 0$, where $0 < \alpha < \infty$, and satisfies certain regularity conditions. $X_1,\cdots, X_n$ are independent random variables with the common density $f(x - \theta), \theta$ an unknown parameter. Let $\hat{\theta}_n$ denote the maximum likelihood estimator of $\theta$, and define $\alpha_n$ by the equation $2\alpha_n^2 = \alpha n \log n$…

单峰密度最大似然估计的可测性与一致性AI 解读

This paper is concerned with maximum likelihood estimates for a large class of families of unimodal densities. The existence of measurable maximum likelihood estimates and the consistency of asymptotic maximum likelihood estimates are proved. By counterexamples it is shown that the conditions which are sufficient for consistency cannot be removed without compensation.

稳健回归：渐近理论、猜想与 Monte Carlo 模拟AI 解读

Maximum likelihood type robust estimates of regression are defined and their asymptotic properties are investigated both theoretically and empirically. Perhaps the most important new feature is that the number $p$ of parameters is allowed to increase with the number $n$ of observations. The initial terms of a formal power series expansion (essentially in powers of $p/n$) show an excellent agreement with Monte Carlo results, in most cases down to 4 observations per parameter.

频数数据的对数线性模型：充分统计量与似然方程AI 解读

A general model is proposed for analysis of frequency tables. This model includes conventional log-linear models for complete and incomplete factorial tables and logit models for quantal response analysis. By use of coordinate-free methods of linear algebra and differential calculus, complete minimal sufficient statistics and likelihood equations for the maximum likelihood estimate are derived. The maximum likelihood estimate is shown to be unique if it exists, and necessary…

若干非标准情形下最大似然估计量的渐近性质（二）AI 解读

In an earlier article, asymptotic properties of maximum likelihood estimators were found in a class of nonstandard cases when three assumptions were satisfied. The third assumption was rather complicated. In this article it is shown that if we strengthen the second assumption slightly, we can dispense with the third assumption entirely.

一类协方差结构模型的研究AI 解读

This article demonstrates the usefulness of analysis of covariance structure procedures for estimating variance components under more general assumptions than are provided in the typical mixed-model analysis of variance. A sequence of eight models is presented based on varying degrees of restrictive assumptions. Maximum likelihood procedures are employed in the estimation of the parameters of the models. The procedures are applied to simulated data and to an empirical…

同质性检验的渐近性质AI 解读

Tests for the homogeneity of samples from the Poisson and Gamma distributions are considered based on the C(α ) procedure of Neyman and on maximum likelihood estimators. These are shown to be equivalent in spite of the fact that the null hypothesis lies on the boundary of the parameter space, which is contrary to the assumptions under which the C(α ) test is derived. Moreover, it is shown that neither procedure has been proved to work unless the disturbing distribution is…

参数随机分散的线性回归AI 解读

Consider a collection of individual linear regression models, in which each individual parameter vector is independently drawn from a common multivariate normal distribution and is fixed over successive observations on that individual. Maximum likelihood estimators of the mean and dispersion of the parameters and of the disturbance variance are derived. These estimators yield empirical Bayes estimators of the individual parameter veotors. The properties of the estimators are…

参数随机分散的线性回归AI 解读

Consider a collection of individual linear regression models, in which each individual parameter vector is independently drawn from a common multivariate normal distribution and is fixed over successive observations on that individual. Maximum likelihood estimators of the mean and dispersion of the parameters and of the disturbance variance are derived. These estimators yield empirical Bayes estimators of the individual parameter veotors. The properties of the estimators are…

含三个及以上自变量的某些多元回归问题中最大似然估计的不可容许性AI 解读

Consider a multiple regression problem in which the dependent variable and (3 or more) independent variables have a joint normal distribution. This problem was investigated some time ago by Charles Stein, who proposed reasonable loss functions for various problems involving estimation of the regression coefficients and who obtained various minimax and admissibility results. In this paper we continue this investigation and establish the inadmissibility of the traditional…

异方差线性模型的估计AI 解读

This article considers the familiar linear model in which the residual vector e has elements e i with expectation 0 but different variances σ2 i . The elements of and the σ2 i are estimated by maximum likelihood under the assumption of a lower bound for the σ2 i of the form 0 < δ2 i ≤ σ2 i so that the likelihood is finite in the restricted parameter space. A second problem is considered in which the y vector splits into k sub-vector y j , such that all elements of y j have…

离散概率函数线性组合的最大似然估计AI 解读

In this article the problem of obtaining the maximum likelihood estimates of the parameters from a special type of linear combination of discrete probability functions is discussed. It is shown that when the sample is completely categorized the estimation problem is no more complicated that that of estimating the parameters of each of the component probability functions separately. When the sample is less than completely classified an iterative procedure must be used to…

Spearman–Kärber 与最大似然均值估计的等价性AI 解读

In this article, we show that two methods of estimating the mean of a distribution using quantal response data are often equivalent. The two estimates considered are the Spearman-Kärber and an estimate discussed in a previous article by the authors [4]. The latter is based on a maximum likelihood solution for a nonparametric problem.

指数族中最大似然与加权最小二乘估计的等价性AI 解读

In this article it is shown that weighted least squares estimators for the coefficients of a multiple regression model are the same as the maximum likelihood estimators when the dependent observations are from a member of the regular exponential class of distributions.

Stein 估计规则及其竞争方法：经验贝叶斯视角AI 解读

Stein's estimator for k normal means is known to dominate the MLE if k ≥ 3. In this article we ask if Stein's estimator is any good in its own right. Our answer is yes: the positive part version of Stein's estimator is one member of a class of “good” rules that have Bayesian properties and also dominate the MLE. Other members of this class are also useful in various situations. Our approach is by means of empirical Bayes ideas. In the later sections we discuss rules for more…

离散概率函数线性组合的最大似然估计AI 解读

In this article the problem of obtaining the maximum likelihood estimates of the parameters from a special type of linear combination of discrete probability functions is discussed. It is shown that when the sample is completely categorized the estimation problem is no more complicated that that of estimating the parameters of each of the component probability functions separately. When the sample is less than completely classified an iterative procedure must be used to…

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摘要暂缺

This paper deals with similarities and differences in the equations defining the full information maximum likelihood and three stage least squares estimators. It shows that the twp sets of equations are similar, the difference being that the two estimators purge the jointly dependent variables differently. Hence, even if three stage least squares is iterated, it will not give an estimator which is the same as the maximum likelihood one. On the other hand, it is quite…

N this paper, I will generalize the modified Newton method previously applied in Chow (1968) to the computation of full-information maximum likelihood estimates of parameters of a system of linear structural equations to the case of a system of nonlinear structural equations. The success of that method for linear systems 1 has stimulated my present attempt to generalize it for nonlinear systems. The subject of maximum likelihood estimation of nonlinear simultaneous equation…