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基于广义 t 分布的回归模型部分自适应估计AI 解读

This paper considers M-estimators of regression parameters that make use of a generalized functional form for the disturbance distribution. The family of distributions considered is the generalized t (GT), which includes the power exponential or Box-Tiao, normal, Laplace, and t distributions as special cases. The corresponding influence function is bounded and redescending for finite “degrees of freedom.” The regression estimators considered are those that maximize the GT…

自回归移动平均过程的若干精确公式AI 解读

This paper demonstrates that for a finite stationary autoregressive moving average process the inverse of the covariance matrix differs from the matrix of the covariances of the inverse process by a matrix of low rank. The formula for the exact inverse of the covariance matrix of the scalar or multivariate process is provided. We obtain approximations based on this formula and evaluate some of the approximate results in the existing literature. Applications to computational…

联立 Probit 模型的有限信息估计与外生性检验AI 解读

A two-step maximum likelihood procedure is proposed for estimating simultaneous probit models and is compared to alternative limited information estimators. Conditions under which each estimator attains the Cramer–Rao lower bound are obtained. Simple tests for exogeneity based on the new two-step estimator are proposed and are shown to be asymptotically equivalent to one another and to have the same local asymptotic power as classical tests based on the limited information…

观测相关情形下的Probit估计AI 解读

Estimation of limited dependent variable models with dependent observations has received relatively little attention due to the computational complexity of the maximum likelihood estimator. We develop a computationally attractive and relatively efficient estimator for this case that utilises the orthogonality conditions. The resulting Generalized Conditional Moment (GCM) estimators can be applied with a known or an unknown disturbance covariance matrix. Although the paper…

扩展拟似然方法的一则注记AI 解读

SUMMARY We study the method of extended quasi-likelihood estimation and inference of a variance function recently proposed by Nelder and Pregibon. The estimates are inconsistent in general, and the test levels can be biased, but in many cases such as the exponential family the inconsistency and bias will not be a major concern. Extended quasi-likelihood is compared with Carroll and Ruppert's pseudo-likelihood method, which gives consistent estimates and, when slightly…

In this paper the asymptotic behaviour of the product limit estimator $F_n$ of an unknown distribution is investigated. We give an approximation of the difference $F_n(x) - F(x)$ by a Gaussian process and also by the average of i.i.d. processes. We get almost as good an approximation of the stochastic process $F_n(x) - F(x)$ as one can get for the analogous problem when the maximum likelihood estimator is approximated by a Gaussian random variable or by the average of i.i.d.…

有偏抽样模型中经验分布的大样本理论AI 解读

Vardi (1985a) introduced an $s$-sample model for biased sampling, gave conditions which guarantee the existence and uniqueness of the nonparametric maximum likelihood estimator $\mathbb{G}_n$ of the common underlying distribution $G$ and discussed numerical methods for calculating the estimator. Here we examine the large sample behavior of the NPMLE $\mathbb{G}_n$, including results on uniform consistency of $\mathbb{G}_n$, convergence of $\sqrt n (\mathbb{G}_n - G)$ to a…

多期条件矩限制所蕴含的效率界AI 解读

In this article we study a class of econometric models that imply a set of multiperiod conditional moment restrictions. These restrictions depend on an unknown parameter vector. We construct an extensive class of consistent, asymptotically normal estimators of this parameter vector and calculate the greatest lower bound for the asymptotic covariance matrices of estimators in this class. In so doing, we extend results reported by Hansen (1985) and Stoica, Söderström, and…

二元回归中的变量测量误差：Berkson情形AI 解读

In binary regression, the predictor variables may be measured with error. The Berkson case of the errors-in-variables problem is considered, under which the values of the predictor variables are set by the experimenter but not achieved exactly. A particular model for this case is considered, with probit regression and normally distributed errors of observation. The regression parameters for intercept and slope are to be estimated. Two estimators are studied, the maximum…

一个考古年代推断问题AI 解读

An archaeological dating problem is presented and analyzed. The analysis is based on a data-generating model, which takes careful account of the various kinds of uncertainty involved in relating observed radiocarbon dates of artifacts to successive chronological beginning and ending dates of significant archaeological phases. In addition to its intrinsic interest as a possible model for many kinds of archaeological data of this type, the model poses some challenging…

二元反应生物测定中的核估计与 Probit 估计AI 解读

A kernel method for the estimation of quantal dose-response curves is considered. In contrast to parametric modeling, this local smoothing method does not require any assumptions beyond smoothness of the dose-response curve and, in this sense, is nonparametric. In finite-sample situations, the kernel estimate of the dose-response curve is not necessarily monotone and, therefore, if the additional assumption of monotonicity of the dose-response curve is made, a monotonized…

相关二元数据的条件Logistic回归模型AI 解读

A class of conditional logistic regression models for clustered binary data is considered. This includes the polychotomous logistic model of Rosner (1984) as a special case. Properties such as the joint distribution and pairwise odds ratio are investigated. A class of easily computed estimating functions is introduced which is shown to have high efficiency compared to the computationally intensive maximum likelihood approach. An example on chronic obstructive pulmonary…

离散观测下广义 Itô 过程的最大似然估计AI 解读

This paper considers the parametric estimation problem for continuous-time stochastic processes described by first-order nonlinear stochastic differential equations of the generalized Itô type (containing both jump and diffusion components). We derive a particular functional partial differential equation which characterizes the exact likelihood function of a discretely sampled Itô process. In addition, we show by a simple counterexample that the common approach of estimating…

时间序列分析的小样本效应：新的渐近理论与估计方法AI 解读

To estimate the parameters of a stationary process, Whittle (1953) introduced an approximation to the Gaussian likelihood function. Although the Whittle estimate is asymptotically efficient, the small sample behavior may be poor if the spectrum of the process contains peaks. We introduce a mathematical model that covers such small sample effects. We prove that the exact maximum likelihood estimate is still optimal in this model, whereas the Whittle estimate and the…

一般条件下因子分析估计量的渐近正态分布AI 解读

Asymptotic properties of estimators for the confirmatory factor analysis model are discussed. The model is identified by restrictions on the elements of the factor loading matrix; the number of restrictions may exceed that required for identification. It is shown that a particular centering of the maximum likelihood estimator derived under assumed normality of observations yields an asymptotic normal distribution that is common to a wide class of distributions of the factor…

截断数据非参数最大似然估计量的若干表示AI 解读

The nonparametric maximum likelihood estimators of the distribution functions of observations in the truncation model are represented as iid mean processes, with a remainder term of order $o(n^{-1/2})$ a.s.

高斯过程协方差的筛估计量AI 解读

Maximum likelihood estimation for the covariance $R$ of a zero-mean Gaussian process is considered, with no assumptions on the covariance or the "time" parameter set $T$. It is shown that the likelihood function is a.s. unbounded in general, and a sieve estimator $\hat{R}$ is constructed. The distribution of $\hat{R}$, considered as a process on $T \times T$, can be described exactly if a certain technical assumption is satisfied concerning the bivariate series expansion of $R$…

方向数据估计量的稳健性AI 解读

Some standard robustness concepts, developed for linear data, are found wanting in the case of directional data. We introduce a standardized bias robustness allowing for uniform robustness considerations of statistics for bounded parameter spaces. Specifically, we verify the nonrobustness in this sense of the directional mean, the directional dispersion and the maximum likelihood estimator of the concentration parameter of the von Mises-Fisher distributions.

一类离散分布的参数正交化AI 解读

The standard contagious distributions (see Douglas 1980) have been used in such varied fields as biology and automobile insurance, often to model various physical phenomena as well as provide a good fit to count data when other models are inadequate. Unfortunately, the parameterizations often used when working with these distributions normally lead to extremely high correlations of the maximum likelihood estimators (MLE's). This tends to lead to mathematical complexities,…

锥约束对数线性模型中 I 投影与最大似然估计的对偶性AI 解读

Important order restrictions and general log-linear models for multinomial experiments can often be expressed by requiring that the vector composed of the logs of the probabilities fall within a closed convex cone. Here we exhibit a duality relationship (by way of a Fenchel duality theorem) between these types of problems and projections in I-divergence geometry. We show that many cone-constrained maximum likelihood estimation problems are exactly equivalent to an I…

利用最大似然预测纪录AI 解读

A maximum likelihood method of fitting a model to a series of records is proposed, using ideas from the analysis of censored data to construct a likelihood function based on observed records. This method is tried out by fitting several models to series of athletics records for mile and marathon races. A form of residual analysis is proposed for testing the models. Forecasting consequences are also considered. In the case of mile records, a steady linear improvement since…

摘要暂缺

用最大似然法预测纪录AI 解读

A maximum likelihood method of fitting a model to a series of records is proposed, using ideas from the analysis of censored data to construct a likelihood function based on observed records. This method is tried out by fitting several models to series of athletics records for mile and marathon races. A form of residual analysis is proposed for testing the models. Forecasting consequences are also considered. In the case of mile records, a steady linear improvement since…

摘要暂缺