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某类指数模型中条件极大似然估计量的渐近行为AI 解读

SUMMARY In this paper we investigate the asymptotic behaviour of the conditional maximum likelihood estimator in an exponential model of order 2 introduced in Bar-Lev and Reiser (1982). This model, with natural parameters θ1 and θ2 (the latter a nuisance parameter), is characterized by expressing θ2 as a particular function of the mixed parameters. A direct proof is given for the asymptotic equivalence of the conditional maximum likelihood estimator and the maximum…

局部渐近设定误差分析AI 解读

An approximation to the inconsistency introduced by imposing an incorrect restriction on a parametric model is given. The approximation can be applied to estimators generated by optimizing any objective function satisfying certain regularity conditions. Examples given include analysis of misspecification in discrete choice and time-series models estimated by maximum likelihood, and in a nonlinear regression model. SPECIFICATION ERROR ANALYSIS in the linear regression model…

误差协方差矩阵非标量时线性模型中的假设检验AI 解读

A WELL DEVELOPED EXACT STATISTICAL THEORY exists for hypothesis testing in the normal linear regression model when the errors are independent and homoscedastic. In the more general case where the error covariance matrix is nonscalar and depends on a set of unknown parameters, exact analysis is difficult and reliance is usually placed on asymptotic approximations for large sample size n. In this paper, higher-order asymptotic expansions are developed for comparing the size…

对 Amemiya 二元 Logit 回归估计论文的评论AI 解读

Amemiya (1980) derived expressions for the $n^{-2}$-order mean squared errors of the maximum likelihood and the minimum logit chi-squared estimators in the dichotomous logit regression model. He numerically evaluated these expressions for a number of specific examples and in all examples found that the minimum chi-squared estimator has smaller $n^{-2}$-order mean squared error. In this paper, we demonstrate examples in which the maximum likelihood estimator has smaller $n^{-2}$…

测量误差协方差矩阵由估计获得时的多元变量误差模型估计AI 解读

The errors-in-variables model in which the unobserved true values satisfy multiple linear restrictions is considered. Under the assumptions that the unobservable true values are normally distributed and that an estimator of the covariance matrix of the measurement error is available, the maximum likelihood estimators are derived. The limiting properties of the estimators are obtained for a wide range of assumptions, including the assumption of fixed true values.

摘要暂缺

受约束二元线性回归系数的截断极大似然估计AI 解读

In a bivariate linear regression model, the constrained maximum likelihood estimator (MLE) of a regression coefficient usually has smaller variance than the unconstrained MLE. This situation can be reversed if both the sample size n and the correlation coefficient ρ of disturbances between two regression equations are small. That is, when both n and ρ are small, the variance of the unconstrained MLE is smaller than the constrained MLE. In this article, a truncated MLE is…

摘要暂缺

自适应分类程序AI 解读

An explicitly computable, necessary, and sufficient condition for the existence of an adaptive classification procedure is obtained. By definition, an adaptive procedure, which classifies a sample as coming from one of alternative distributions known only up to a finite-valued nuisance parameter, is required to have the same asymptotic behavior of error probability for these families as asymptotically optimal rules for each of the families. We investigate the conditions…

大样本随机删失下若干极大似然估计量的性质AI 解读

In the case the survival distribution of a life length X is of the form ln[1 - Fx (x)] = -αQ(βx) for x > 0, where the hazard function Q is known but α or β or both are unknown, the asymptotic distribution of the maximum likelihood estimators of the shape and scale parameters is found for large randomly censored samples. The covariance matrix of is expressed in terms of the distribution of the random variable that can be observed, namely, Y = min(X, T); here T is the random…

随机系数自回归模型导论AI 解读

1 Introduction.- 1.1 Introduction.- Appendix 1.1.- Appendix 1.2.- 2 Stationarity and Stability.- 2.1 Introduction.- 2.2 Singly-Infinite Stationarity.- 2.3 Doubly-Infinite Stationarity.- 2.4 The Case of a Unit Eigenvalue.- 2.5 Stability of RCA Models.- 2.6 Strict Stationarity 37 Appendix 2.1.- 3 Least Squares Estimation of Scalar Models.- 3.1 Introduction.- 3.2 The Estimation Procedure.- 3.3 Strong Consistency and the Central Limit Theorem.- 3.4 The Consistent Estimation of…

摘要暂缺

受约束双变量线性回归系数的截断极大似然估计AI 解读

In a bivariate linear regression model, the constrained maximum likelihood estimator (MLE) of a regression coefficient usually has smaller variance than the unconstrained MLE. This situation can be reversed if both the sample size n and the correlation coefficient ρ of disturbances between two regression equations are small. That is, when both n and ρ are small, the variance of the unconstrained MLE is smaller than the constrained MLE. In this article, a truncated MLE is…

联立方程估计量的结构：向非正态扰动的推广AI 解读

A general linear simultaneous equation system with a multivariate Student t disturbance vector is considered. The normal equations of the corresponding maximum likelihood estimator are used as estimator generating equations to introduce a new class of estimators. Properties of large subclasses of these estimators are determined for disturbance vectors other than the multivariate Student t.

伪极大似然方法：泊松模型的应用AI 解读

Pseudo maximum likelihood techniques are applied to basic Poisson models and to Poisson models with specification errors. In the latter case it is shown that consistent and asymptotically normal estimators can be obtained without specifying the p.d.f. of the disturbances. These estimators are compared both from the finite sample and the asymptotic point of view. Quasi generalized PML estimators, which asymptotically dominate all PML estimators, are also proposed. Finally,…

因变量存在测量误差的删失正态回归AI 解读

When zero mean measurement error is added to the dependent variable for the nonlimit observations of the censored normal regression model, the conventional maximum likelihood estimator (Tobit) is inconsistent. Correct maximum likelihood estimation appears to be computationally difficult under various specifications for the distribution of the measurement error. Estimators based on either the expectation function or the conditional expectation function for uncensored…

伪极大似然方法：理论AI 解读

Estimators obtained by maximizing a likelihood function are studied in the case where the true p.d.f. does not necessarily belong to the family chosen for the likelihood function. When such a procedure is applied to the estimation of the parameters of the first order moments, it is possible to prove a necessary and sufficient condition for its consistency. Asymptotic normality is shown as well as the existence of a lower bound for the asymptotic covariance matrix. It is also…

家庭数据中类间相关系数的估计AI 解读

The maximum likelihood estimates of the parent-child interclass correlation and other parameters from familial data when the families have unequal numbers of offspring is given. Also given are two alternative sets of estimates which are easier to compute than the maximum likelihood estimates. Using these estimates, a test for the interclass correlation to be zero requires only the ordinary Student's t-distribution. Similarly other tests use only known distributions.

无符号方向数据的无分布区间估计方法AI 解读

A method of moments is suggested for large samples of unsigned directional data. The point estimators obtained coincide with the natural estimates obtained from maximum likelihood estimation if the data have a Bingham distribution. However, the calculations necessary for interval and regional estimation are considerably simpler. The statistical analysis is based upon the asymptotic sampling properties of principal components in nonnormal populations (Davis, 1977; Tyler,…

二元回归模型中的变量测量误差AI 解读

We consider binary regression models when some of the predictors are measured with error. For normal measurement errors, structural maximum likelihood estimates are considered. We show that if the measurement error is large, the usual estimate of the probability of the event in question can be substantially in error, especially for high risk groups. In the situation of large measurement error, we investigate a conditional maximum likelihood estimator and its properties.

一个非参数最大似然估计问题的简单解法AI 解读

Three approaches to a nonparametric maximum likelihood problem are considered. One, based on the method of "sieves", is shown to include the other two. The sieve considered is a double exponential convolution sieve. A closed form solution is given for certain values of the sieve parameter.

位置估计量与分布的分散程度AI 解读

In the location estimation problem, translation equivariant estimators are considered. It is shown that under a mild regularity condition the distribution of such estimators is more spread out than a particular distribution which is defined in terms of the sample size and the density of the i.i.d. observations. Some consequences of this so-called spread-inequality are discussed, namely the Cramer-Rao inequality, an asymptotic minimax inequality and the efficiency of the…

线性统计关系的估计AI 解读

This paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships, factor analysis, and simultaneous equations models. The emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators (under normality) in the different models. In the first two lectures the observable vector is decomposed into a "systematic part" and a random error; the systematic part…

单样本寿命表数据的拟合优度检验AI 解读

Grouped censored data are common in life testing, medical trials, and other fields. Individuals, subject to a disease, have their lifetimes recorded as belonging to a certain interval. If the individuals are censored or removed before death, then it is only known that their lifetimes were at least as great as the beginning of the interval in which the individuals were censored. A goodness-of-fit problem is to test the agreement of a hypothesized survival curve with the…