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两步计量经济模型的估计与推断AI 解读

A commonly used procedure in a wide class of empirical applications is to impute unobserved regressors, such as expectations, from an auxiliary econometric model. This two-step (T-S) procedure fails to account for the fact that imputed regressors are measured with sampling error, so hypothesis tests based on the estimated covariance matrix of the second-step estimator are biased, even in large samples. We present a simple yet general method of calculating asymptotically…

非线性回归中渐近分布的适用性与曲率AI 解读

SUMMARY In a non-linear regression model, correction terms for the asymptotic distribution of the maximum likelihood estimator are found. They can all be evaluated by the parameter dependent part of Beale's (1960) measure of non-linearity and some of the terms can be evaluated by Bates and Watts (1980) parameter dependent curvature in specific directions. The theory is illustrated by examples.

有限混合模型中的估计与假设检验AI 解读

SUMMARY Finite mixture models are a useful class of models for application to data. When sample sizes are not large and the number of underlying densities is in question, likelihood ratio tests based on joint maximum likelihood estimation of the mixing parameter, λ, and the parameter of the underlying densities, θ, are problematical. Our approach places a prior distribution on λ and estimates θ by maximizing the likelihood of the data given θ with λ integrated out.…

替代异常值模型下限制最大似然估计的一则札记AI 解读

SUMMARY For single outliers in normal theory fixed effects models a mean slippage model is commonly used. An alternative is to model the outlier as arising from an unknown observation with inflated variance. Maximum likelihood estimates for the position of the outlier under the two models need not agree. This paper considers maximizing a restricted part of the likelihood to estimate the variance parameters and characterizes these estimates in terms of standard least squares…

一步与两步 M 估计量的收敛速度：最大似然与 Pitman 估计的应用AI 解读

A one-step version $M^{(1)}_n$ and a two-step version $M^{(2)}_n$ of a general $M$-estimator $M_n$ are suggested such that $M_n - M^{(1)}_n = O_p(n^{-1})$ and $M_n - M^{(2)}_n = O_p(n^{-3/2})$ for every $n^{1/2}$-consistent initial estimator and under some regularity conditions. In the special case of maximum likelihood estimation, this among other yields that the second-order efficiency properties of $M^{(2)}_n$ coincide with those of $M_n$. An application to the Pitman…

近似最大似然估计的强一致性及其非参数应用AI 解读

Wald's general analytic conditions that imply strong consistency of the approximate maximum likelihood estimators (AMLEs) have been extended by Le Cam, Kiefer and Wolfowitz, Huber, Bahadur, and Perlman. All these conditions use the log likelihood ratio of the type $\log\lbrack f(x, \theta)/f(x, \theta_0)\rbrack$, where $\theta_0$ is the true value of the parameter. However these methods usually fail in the nonparametric case. Thus, in this paper, for each $\theta \neq \theta_0$…

利用经验部分贝叶斯推断提高估计效率AI 解读

Empirical partially Bayes methods are considered as a means of improving efficiency in a class of problems in which the number of nuisance parameters increases to infinity. In the method used, the parameter of interest is estimated in an asymptotically unbiased way while James-Stein shrinkage is applied to the nuisance parameter estimates. When the shrinkage estimators are carefully chosen, this yields estimators generally more efficient than maximum likelihood. In the…

聚合、结构变化与截面估计AI 解读

This article characterizes the local effects of parametric behavioral model change on relationships between aggregate variables, and it presents consistent estimators of such effects using cross-section data. Two equivalent interpretations of model-change effects are given: an “average-marginal” formulation and a cross-section regression formulation. The relation between model-change effects and maximum likelihood estimation of the behavioral parameters is explained.…

用 EM 算法拟合双重抽样分类数据的对数线性模型AI 解读

Double-sampling experiments can be expressed as incomplete multiway contingency tables and analyzed by using techniques appropriate for fitting log-linear models. The framework described can be applied to experiments with any number of factors and measurement devices. Maximum likelihood estimation via the EM algorithm leads to straightforward expressions for covariances of estimates of the parameters and functions of the parameters.

用于多层分析的分层逻辑回归模型AI 解读

A hierarchical logistic regression model is proposed for studying data with group structure and a binary response variable. The group structure is defined by the presence of micro observations embedded within contexts (macro observations), and the specification is at both of these levels. At the first (micro) level, the usual logistic regression model is defined for each context. The same regressors are used in each context, but the micro regression coefficients are free to…

用 EM 算法拟合双重抽样分类数据的对数线性模型AI 解读

Double-sampling experiments can be expressed as incomplete multiway contingency tables and analyzed by using techniques appropriate for fitting log-linear models. The framework described can be applied to experiments with any number of factors and measurement devices. Maximum likelihood estimation via the EM algorithm leads to straightforward expressions for covariances of estimates of the parameters and functions of the parameters.

高级计量经济学：通向文献的桥梁AI 解读

TOPICS IN LARGE SAMPLE THEORY AND APPROXIMATION METHODS. A Review of Asymptotic Distribution Theory and Maximum Likelihood Estimation. Methods of Approximating Distribution Functions, Density Functions, and Moments. TOPICS IN TIME SERIES ANALYSIS. An Introduction to Time Series Analysis. Identification, Estimation, and Prediction in Time Series Models. The Relationship Between Time Series Models and Econometric Models. TOPICS IN ESTIMATION UNDER A QUADRATIC LOSS CRITERION.…

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临床试验两期交叉设计中不完整数据的分析AI 解读

A procedure for analysing a simple two-period crossover design is proposed when some observations at the second treatment period are missing. Using all available data, the maximum likelihood estimators of the parameters are obtained and approximate tests proposed under the assumption that the data come from bivariate normal populations. The performances of these tests are compared with those of Grizzle's tests which require complete pairs of observations, using Monte Carlo…

直接效用函数中随机偏好变动的序列相关理论AI 解读

Methods of maximum-likelihood search (eg., Hildreth-Lu) for single equations models with autocorrelated disturbances are not easily extended to the multi-equation systems encountered in econometric studies of consumer demand. The obstacle is the large dimension of the space of independent serial correlation coefficients to be partitioned and searched. This paper treats stochastic disturbance vectors in demand/expenditure systems as functions of random disturbances in…

参数模型一致估计的统一理论AI 解读

We present a general theory of consistent estimation for possibly misspecified parametric models based on recent results of Domowitz and White. This theory extends the unification of Burguete, Gallant, and Souza by allowing for heterogeneous, time-dependent data and dynamic models. The theory is applied to yield consistency results for quasi-maximum-likelihood and method of moments estimators. Of particular interest is a new generalized rank condition for identifiability.

存在干扰参数时置信限的渐近展开及应用AI 解读

SUMMARY Series expansions for confidence limits based on consistent estimators are obtained in the presence of nuisance parameters. The maximum likelihood estimator is treated as a special case and the necessary characteristics of its sampling distribution are obtained in terms of basic quantities derivable from the likelihood function. The theory is applied to the problem of setting separate confidence limits for the scale and shape parameters of the Weibull distribution.…

正态混合分布最大似然估计的约束表述AI 解读

The method of maximum likelihood leads to an ill-posed optimization problem in the case of a mixture of normal distributions. Estimation in the univariate case is reformulated using simple constraints into an optimization problem having a strongly consistent, global solution.

渐近辅助性的二阶研究AI 解读

The paper deals with approximate ancillarity as discussed by Efron and Hinkley (1978). In the multivariate i.i.d. case we derive the second-order Edgeworth expansion of the MLE given a normalized version of the second derivative of the log-likelihood at its maximum. The expansion agrees with the one derived by Amari (1982a) for curved exponential families, but holds for any family satisfying the regularity conditions given in the paper. It is shown that the Fisher…

积分比值的一个实用不等式及其极大似然估计应用AI 解读

A generalization of a well-known covariance inequality is proved and is used to furnish sufficient conditions for the strict concavity of the log-likelihood of an observable random variable Y as a function of a real parameter θ that governs the distribution of an unobservable random variable X on which the distribution of Y depends in a known way.

基于 II 型删失数据的极大似然及相关估计量的渐近性质AI 解读

Some simple procedures are provided for establishing the asymptotic normality and uniform strong convergence of a class of functions that arise in the context of estimating parameters from a Type II censored sample. These lead to an elementary yet rigorous treatment of the asymptotic properties of maximum likelihood estimators based on Type II censored data. Further applications include the treatment of asymptotics of some modified maximum likelihood (MML) estimators. In…

秩删失数据的最大似然回归AI 解读

Linear regression is a common method for analyzing continuous, cardinal data, but it is inappropriate when the dependent variable is an ordinal ranking. The model proposed for analyzing these data sets is the general linear model u = Xβ + ε, where the rank of the dependent variable u is observed instead of its value. A description is given for a numerical algorithm to evaluate the likelihood function that is efficient enough to permit maximum likelihood estimation of…

计数过程的统计分析AI 解读

1. One-Dimensional Counting Processes.- 1.1. Probabilities on (0,?].- 1.2. The definition of one-dimensional counting processes.- 1.3. Construction of canonical counting processes.- 1.4. Intensities for canonical counting processes.- 1.5. Martingale decompositions for canonical counting processes.- 1.6. Statistical models and likelihood ratios.- Notes.- Exercises.- 2. Multivariate Counting Processes.- 2.1. Definition and construction of multivariate counting processes.- 2.2.…

秩删失数据的最大似然回归AI 解读

Linear regression is a common method for analyzing continuous, cardinal data, but it is inappropriate when the dependent variable is an ordinal ranking. The model proposed for analyzing these data sets is the general linear model u = Xβ + ε, where the rank of the dependent variable u is observed instead of its value. A description is given for a numerical algorithm to evaluate the likelihood function that is efficient enough to permit maximum likelihood estimation of…