论文检索

自回归移动平均模型马尔可夫表示的参数估计AI 解读

Tuan (1978) discussed the approximate maximum likelihood estimation of the parameters of the Markovian representation of the autoregressive-moving average model. He considered an indirect method, using the equivalent quasiautoregressive moving average form, the parameters of which are in one to one correspondence with those of the Markovian representation. A method of finding exact joint maximum likelihood estimates of the parameters and the initial state of the process is…

非参数多元二元判别AI 解读

Aitchison & Aitken (1976) introduced a novel and ingenious nonparametric method for estimating probabilities in a multidimensional binary space. The technique is designed for use in multivariate binary discrimination. Their estimator depends crucially on an unknown smoothing parameter λ, and Aitchison & Aitken proposed a maximum likelihood method for determining λ from the sample. Unfortunately this leads to an adaptive estimator which can behave very erratically when there…

特定协方差矩阵的表示及其渐近效率应用AI 解读

Although maximum likelihood estimates are asymptotically efficient, they are often very hard to find. Replacement of some, but not all, of the equations in the maximum likelihood system may make it more manageable. The covariance matrices of the new estimator and of the estimating functions will have special structure in relation to the information matrix. These relationships are characterized and various properties that pertain to multiparameter efficiency are developed.…

低响应概率下逻辑回归的样本量计算AI 解读

The Fisher information matrix for the estimated parameters in a multiple logistic regression can be approximated by the augmented Hessian matrix of the moment-generating function for the covariates. The approximation is valid when the probability of response is small. With its use one can obtain a simple closed-form estimate of the asymptotic covariance matrix of the maximum likelihood parameter estimates, and thus approximate sample sizes needed to test hypotheses about the…

某类协方差矩阵的表示及其渐近效率应用AI 解读

Although maximum likelihood estimates are asymptotically efficient, they are often very hard to find. Replacement of some, but not all, of the equations in the maximum likelihood system may make it more manageable. The covariance matrices of the new estimator and of the estimating functions will have special structure in relation to the information matrix. These relationships are characterized and various properties that pertain to multiparameter efficiency are developed.…

隐式非线性联立方程模型中最大似然估计框架下的统计推断AI 解读

A. Ronald Gallant, Alberto Holly, Statistical Inference in an Implicit, Nonlinear, Simultaneous Equation Model in the Context of Maximum Likelihood Estimation, Econometrica, Vol. 49, No. 2 (Mar., 1981), p. 554

降秩回归与典型分析AI 解读

SUMMARY We show that maximum-likelihood analysis of the reduced-rank regression model exploits a fundamental inequality result of matrix theory when a normally distributed error structure with unknown covariance is assumed. This approach closely parallels the corresponding analysis when the covariance matrix is known (Davies and Tso, 1980) and demonstrates straightforwardly the intimate connection between reduced-rank regression and canonical analysis. A geometric…

圆形结构模型AI 解读

SUMMARY This paper deals with consistent estimation of the structural parameters of the circular structural model. Identifiability is proved and the difficulties of dealing with the structural model in practice mentioned. A uniform distribution is then assumed for the angular variables and maximum likelihood estimation of the parameters examined. Also discussed are use of an approximation to the ratio of modified Bessel functions, asymptotic behaviour of the estimators as…

不可识别分布中最大似然估计的一致性札记AI 解读

The results of Wald on the consistency of the maximum likelihood estimate are extended. Applications are made to mixture distributions and to clustering when the number of clusters is not known.

多元变量含误差回归模型的估计：大样本结果AI 解读

In a multivariate "errors in variables" regression model, the unknown mean vectors $\mathbf{u}_{1i}: p \times 1, \mathbf{u}_{2i}: r \times 1$ of the vector observations $\mathbf{x}_{1i}, \mathbf{x}_{2i}$, rather than the observations themselves, are assumed to follow the linear relation: $\mathbf{u}_{2i} = \alpha + B\mathbf{u}_{1i}, i = 1,2,\cdots, n$. It is further assumed that the random errors $\mathbf{e}_i = \mathbf{x}_i - \mathbf{u}_i, \mathbf{x}'_i = (\mathbf{x}'_{1i}, \mathbf{x}'_{2i}), \mathbf{u}'_i = (\mathbf{u}'_{1i}, \mathbf{u}'_{2i})$…

匹配病例对照研究与死亡时刻并列生存研究的似然计算AI 解读

A recursion is presented which permits rapid computation of a conditional likelihood function which arises in matched case-control studies and survival studies with tied death times. An example with seven parameters and ten large strata, the largest of which contains 29 cases and 52 controls, illustrates the feasibility of the conditional maximum likelihood solution. These methods may be specialized to permit rapid calculation of the conditional maximum likelihood estimate…

一阶移动平均模型最大似然估计量的小样本性质AI 解读

In this paper we discuss finite sample properties of the maximum likelihood estimator θ^ in the first-order moving average model. We give a theoretical explanation for the concentration of θ^ values at the invertibility boundary. We derive the exact distribution of θ^ for sample size n=2 which is found to be of mixed type. For general n we give approximations for pr (⁠θ^=1).

一类误差相关的双向方差分析模型的最大似然估计AI 解读

A two-way analysis of variance model with correlated errors in one classification is discussed. It is assumed that the p measurements in each row have a general covariance matrix Σ The maximum likelihood estimates of the row and column parameters as well as of the covariance matrix are obtained and their asymptotic distribution are discussed. Finally, the likelihood ratio test statistics for the various hypotheses in a two-way layout are given.

指数族混合模型中条件最大似然估计与置信限的效率AI 解读

In a previous paper (Basawa, 1981) efficient conditional tests were discussed for mixture experiments involving dependent observations. The present paper is devoted to a study of the performance, in large samples, of a conditional maximum likelihood estimator and of a confidence limit for a parameter in a model specified by a mixture of a two-parameter exponential family. The conditional estimator proposed in the paper is free from the mixing distribution, and is efficient…

家族数据分析的线性模型方法AI 解读

A linear-model approach is proposed for deriving the maximum likelihood estimates of the mother–sib interclass correlation and other parameters from familial data when the families have unequal numbers of offspring. It leads to an algorithm which involves the maximization of an explicit function of a variable for estimating one parameter and direct substitutions for other parameters. The algorithm is believed to be much simpler and more practical than that proposed by Rosner…

二元响应数据实现可加性的两类变换AI 解读

Two families of power transformations for probabilites are introduced to model symmetric and asymmetric departures from the logistic model. The aim is to provide, in a comprehensive way, a representation of alternative scales in terms of which to carry out the analysis of binary response data. Maximum likelihood methods are empolyed to estimate an appropriate transformation using GLIM. Tests for detection of symmetric and asymmetric departures are proposed.

多重匹配设计下的相对风险估计AI 解读

Under multiple matching, relative risk from a rare disease is estimated in a retrospective design. Maximum likelihood estimation is carried out using an unconditional probability model. In addition, this model is used to derive a new estimator of relative risk which is noniterative but is as efficient, asymptotically, as the maximum likelihood estimator.

稀疏数据下的优势比估计量AI 解读

The properties of four commonly used estimators of the odds ratio are studied under a large-sample scheme in which the number of 2 × 2 tables increases but the possible marginal configurations remain fixed. Neither the unconditional maximum likelihood nor the empirical logit estimators converge to the true odds ratio; their asymptotic bias is computed for certain special cases of interest. The conditional maximum likelihood and Mantel-Haenszel estimators, which are…

线性变换估计的大样本结果AI 解读

We obtain the asymptotic covariance matrix of the maximum likelihood estimators of the coefficients in a linear functional relationship between two vector variables observed with error. The matrix cannot be found by the usual method of inverting the information matrix due to the presence of incidental parameters. The joint asymptotic distribution of the estimators is shown to be normal under some mild conditions on the incidental parameters. A consistent estimator of the…

自回归移动平均模型马尔可夫表示的参数估计AI 解读

Tuan (1978) discussed the approximate maximum likelihood estimation of the parameters of the Markovian representation of the autoregressive-moving average model. He considered an indirect method, using the equivalent quasiautoregressive moving average form, the parameters of which are in one to one correspondence with those of the Markovian representation. A method of finding exact joint maximum likelihood estimates of the parameters and the initial state of the process is…

离散分布的一类平滑估计量AI 解读

This paper presents a class of smooth weight function estimators for discrete distributions. Any estimator in the class depends on choosing a parameterized set of weights. The resulting estimators are strongly consistent and asymptotically normal under mild regularity conditions. A general procedure for choosing the weight function smoothing parameter is given along with specific solutions in some cases. Mean squared error comparisons with the maximum likelihood estimator…

关于非参数多元二元判别AI 解读

Aitchison & Aitken (1976) introduced a novel and ingenious nonparametric method for estimating probabilities in a multidimensional binary space. The technique is designed for use in multivariate binary discrimination. Their estimator depends crucially on an unknown smoothing parameter λ, and Aitchison & Aitken proposed a maximum likelihood method for determining λ from the sample. Unfortunately this leads to an adaptive estimator which can behave very erratically when there…

封闭总体多次重捕抽样的贝叶斯分析AI 解读

This paper considers from a Bayesian viewpoint inferences about the size of a closed animal population from data obtained by a multiple-recapture sampling scheme. The method developed enables prior information about the population size and the catch probabilities to be utilized to produce considerable improvements in certain cases on ordinary maximum likelihood methods. Several ways of expressing such prior information are explored and a practical example of the uses of…

基于排序集样本的二元正态总体相关系数推断AI 解读

Ranked set sampling was first used to obtain an improved estimate of a population mean. This technique is useful when a small random sample can be visually ordered easily and fairly accurately, but exact measurement of an observation is difficult or expensive. The sampling method is generalized and applied to estimation of the correlation coefficient ρ of a bivariate normal random vector (X, Y). The asymptotic variance of the maximum likelihood estimator of ρ based only on…