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利用迭代广义最小二乘分析多层混合线性模型AI 解读

Models for the analysis of hierarchically structured data are discussed. An iterative generalized least squares estimation procedure is given and shown to be equivalent to maximum likelihood in the normal case. There is a discussion of applications to complex surveys, longitudinal data, and estimation in multivariate models with missing responses. An example is given using educational data.

双变量泊松分布的偶数点估计AI 解读

Estimation of the parameters in the bivariate Poisson distribution by the methods of maximum likelihood, moments and double zero proportion was considered by Holgate (1964). An alternative estimation procedure, the even points method, is studied, asymptotic efficiencies are examined and comparisons with moment estimators are given.

分数差分时间序列建模AI 解读

Aspects of model building using fractionally differenced autoregressive-moving average processes are discussed. An algorithm for approximate maximum likelihood estimation is outlined and the large-sample distribution of the maximum likelihood estimates is derived. The large-sample distribution of the residual autocorrelations is also derived and a modified portmanteau test statistic is obtained for checking model adequacy.

使用广义线性模型分析纵向数据AI 解读

This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for niultivariate Gaussian outcomes. Asymptotic theory…

含测量误差样本的估计问题AI 解读

For $x \in \mathbb{R}$ let $N_\alpha(x) := m\alpha, \operatorname{iff} x \in (\alpha m - \alpha/2, \alpha m + \alpha/2\rbrack$. For a sample $X_1,\ldots, X_n$ we mainly study the asymptotic properties of the estimators $\bar{N}_\alpha := 1/n\sum^n_{i = 1} N_\alpha(X_i)$ and $S^2_\alpha := 1/(n - 1)\sum^n_{i = 1}(N_\alpha(X_i) - \overline{N}_\alpha)^2$ for $\alpha = \alpha_n \rightarrow 0,$ as $n \rightarrow \infty.$ For example, if $E(X^2) < \infty, E(e^{itX}) = o(|t|^{-k}),(|r| \rightarrow\infty)$…

广义样条平滑中选择平滑参数的 GCV 与 GML 比较AI 解读

The partially improper prior behind the smoothing spline model is used to obtain a generalization of the maximum likelihood (GML) estimate for the smoothing parameter. Then this estimate is compared with the generalized cross validation (GCV) estimate both analytically and by Monte Carlo methods. The comparison is based on a predictive mean square error criteria. It is shown that if the true, unknown function being estimated is smooth in a sense to be defined then the GML…

Logistic 回归中的协变量测量误差AI 解读

In a logistic regression model when covariates are subject to measurement error the naive estimator, obtained by regressing on the observed covariates, is asymptotically biased. We introduce a bias-adjusted estimator and two estimators appropriate for normally distributed measurement errors -a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency. The four proposals are studied asymptotically under conditions which are…

基于自洽性的不完整数据广义最大似然估计的大样本研究AI 解读

Self-consistent estimators for estimating distribution functions from incomplete data are presented. In many cases these estimators are also generalized maximum likelihood estimators. In this paper we discuss the theoretical properties of such estimators: existence, uniform consistency, law of the iterated logarithm, and weak convergence. Applications to the product limit estimator for right-censored data and to the estimator proposed by Turnbull (1974, 1976) for doubly…

N 个随机有序变量生存函数的极大似然估计AI 解读

Very often distributions will exist that logically should satisfy linear stochastic ordering requirements. For example, if a mechanical device is improved through N stages, the corresponding survival functions should be linearly stochastically ordered. Nevertheless, estimates may not totally reflect this stochastic ordering because of the inherent variability of the observations. Here we characterize the maximum likelihood estimates of the survival functions subject to…

潜在群体效应的估计AI 解读

Conventional methods of multivariate normal analysis do not apply when the variables of interest are not observed directly but must be inferred from fallible or incomplete data. A method of estimating such effects by marginal maximum likelihood, implemented by means of an EM algorithm, is proposed. Asymptotic standard errors and likelihood ratio tests of fit are provided. The procedures are illustrated with data from the administration of the Armed Services Vocational…

二元响应数据的高效序贯设计AI 解读

A class of sequential designs for estimating the percentiles of a quantal response curve is proposed. Its updating rule is based on an efficient summary of all of the data available via a parametric model. The logit-MLE version of the proposed designs can be viewed as a natural analog of the Robbins—Monro procedure in the case of binary data. It is shown to be asymptotically consistent, optimal, and nonparametric via its connection with the latter procedure. For certain…

一阶自相关误差下线性回归估计量的效率比较AI 解读

This article compares several estimators for linear regression models with first-order autocorrelated errors. Asymptotic variances of the estimators of regression coefficients are obtained up to order T −2 for the maximum likelihood, the iterated Prais-Winsten, and the iterated Cochrane—Orcutt methods. It is shown that the first two methods are equivalent in efficiency and that the last is less efficient. This loss in efficiency is due to the effect of the initial…

检验误差：有限总体中整数参数的极大似然估计AI 解读

In a probability model for possible errors in the inspection of a finite lot containing defective items, it is shown how maximum likelihood estimation is affected by whether the sampling is carried out with or without replacement. These changes are examined by developing a method for simultaneous maximization over an integer and a scalar parameter. A new method for the bounding of the integer solution is introduced. The results show that the parameter estimates in the…

Markov 假设下面板数据的分析AI 解读

Methods for the analysis of panel data under a continuous-time Markov model are proposed. We present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models, and for other process characteristics such as mean sojourn times and equilibrium distributions. Generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented, and…

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依赖数据下的优势比推断AI 解读

When data can be presented as a series of k 2×2 tables with cell counts (xi ,ni−xi, yi, mi−yi), it is often assumed that xi and yi are binomially distributed. This paper deals with inference for the common odds ratio Ψ when the binomial assumption is invalid. When k increases, the consistency and asymptotic normality of the Mantel & Haenszel (1959) estimator is derived. The conditional maximum likelihood estimator is shown to be inconsistent and the asymptotic bias is…

存在相关测量误差的线性结构关系估计AI 解读

Maximum likelihood estimators for model parameters in linear structural relationships having correlated measurement errors are presented. Comparisons between asymptotic mean squared errors of least squares and maximum likelihood estimators of the slope parameter indicate that the least squares estimator is only preferable when the slope parameter is sufficiently small relative to the ratio of error standard deviations; however, unlike structural relationships having…

Maximum likelihood procedures for analysing mixed continuous and categorical data with missing values are presented. The general location model of 01kin & Tate (1961) and extensions introduced by Krzanowski (1980, 1982) form the basis for our methods. Maximum likelihood estimation with incomplete data is achieved by an application of the EM algorithm (Dempster, Laird & Rubin, 1977). Special cases of the algorithm include Orchard & Woodbury's (1972) algorithm for incomplete…

序列相关的一般分析框架AI 解读

In this paper the testing and estimation problems are discussed in the case of serial correlation. Various models are particular cases of the general framework considered: the nonlinear simultaneous equations models, the probit models, the tobit models, the disequilibrium models, the frontier models, etc. In this context, it is shown that the score test can be written explicitly and that the statistic obtained is a generalization of that of Durbin and Watson; moreover, the…

证明中心极限定理的新方法AI 解读

This paper describes some techniques for proving asymptotic normality of statistics defined by maximization of random criterion function. The techniques are based on a combination of recent results from the theory of empirical processes and a method of Huber for the study of maximum likelihood estimators under nonstandard conditions.

The presence of farm programs should directly affect the expectations of producers. This paper analyzes the formation of price expectations when price supports constitute an effective lower bound on the distribution of the expectations. We first investigate what the expected price would be if the usual rational expectations formula is used. This leads to a relationship that is not estimable. We suggest two alternatives -one based on a tobit approximation and the other based…

使用加权工具变量的联立方程模型稳健估计AI 解读

IN THIS PAPER we present a weighted-instrumental-variables estimator that is resistant2 to heavy-tailed errors, aberrant data in either the endogenous or exogenous variables, and certain other model failures. The estimator is analogous to the weighted-least-squares approach to robustness proposed by Krasker and Welsch [21] for ordinary regression. We will discuss the theory that motivated this estimator, derive some of its properties, describe our computational algorithm,…

非线性预算集的计量经济学AI 解读

This article surveys the development of nonparametric models and methods for estimation of choice models with nonlinear budget sets.The discussion focuses on the budget set regression, that is, the conditional expectation of a choice variable given the budget set.Utility maximization in a nonparametric model with general heterogeneity reduces the curse of dimensionality in this regression.Empirical results using this regression are different from maximum likelihood and give…

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