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Admissibility in Discrete and Continuous Invariant Nonparametric Estimation Problems and in their Multinomial Analogs

离散、连续不变非参数估计及多项分布对应问题的可容许性

Discrete and multinomial analogs are defined for classical (continuous) invariant nonparametric problems of estimating the sample cumulative distribution function (sample c.d.f.) and the sample median. Admissibility of classical estimators and their analogs is investigated. In discrete (including multinomial) settings the sample c.d.f. is shown to be an admissible estimator of the population c.d.f. under the invariant weighted Cramer-von Mises loss function $L_1(F, \hat{F}) = \int \big\lbrack (F(t) - \hat{F}(t))^2/(F(t)(1 - F(t))) \big\rbrack dF(t).$…

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A Recursive Regression for High-Dimensional Models, with Application to Growth Curves and Repeated Measures

高维模型的递归回归及其在生长曲线与重复测量中的应用

A fixed-effects formulation of repeated-measures and growth-curve problems usually leads to an unwieldy linear model, so mixed models are widely used for inference that the conditional linear error model could otherwise support with weaker distributional assumptions. Very high-dimensional regressions (not necessarily arising this way) can be fitted by the proposed alternating algorithm, which partitions the design matrix into singly manageable strips and recursively calls a…

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The Cost of Generalizing Logistic Regression

推广 Logistic 回归的代价

Binary-response regression models in which the link function is a family defined by one or more unknown shape parameters are considered. Detailed attention is given to the two single-parameter families proposed by Aranda-Ordaz (1981) that incorporate the logistic, linear, and complementary log-log link functions as special cases. One model is a symmetric family of alternatives to the logistic shape and the second model is an asymmetric family. The increase in variance of…

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Newton—Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measures Data

重复测量线性混合效应模型的 Newton–Raphson 与 EM 算法

We develop an efficient and effective implementation of the Newton—Raphson (NR) algorithm for estimating the parameters in mixed-effects models for repeated-measures data. We formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by Jennrich and Schlüchter (1986) to speed convergence and ensure a positive-definite covariance matrix for the random effects at each iteration. We use…

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Estimating Vector Autoregressions with Panel Data

利用面板数据估计向量自回归模型

This paper considers estimation and testing of vector autoregressio n coefficients in panel data, and applies the techniques to analyze the dynamic relationships between wages an d hours worked in two samples of American males. The model allows for nonstationary individual effects and is estimated by applying instrumental variables to the quasi-differenced autoregressive equations. The empirical results suggest the absence of lagged hours in the wage forecasting equation.…

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Nonparametric Analysis of Technical and Allocative Efficiencies in Production

生产中技术效率与配置效率的非参数分析

In this paper we extend Varian's (1984) nonparametric production analysis to situations when the set of observed output, input, and price data is not consistent with profit maximization for at least one firm. In such cases, Varian's results imply that no production possibility set containing all observations can rationalize the observed data. We identify each firm whose performance, given the prices faced by it, may be found consistent with profit maximization relative to…

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Limited information estimators and exogeneity tests for simultaneous probit models

联立 Probit 模型的有限信息估计与外生性检验

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…

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Probit with Dependent Observations

观测相关情形下的Probit估计

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…

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The Measurement of the Economic Benefits of Infrastructure Services

基础设施服务经济收益的度量

1. Introduction.- 2. A Simple Producer Benef it Measure.- 3. Willingness to Pav Functions and Marginal Cost Functions.- 4. Approximate Benefit Measures.- 5. Problems with the Producer Benefit Measure.- 5.1. Static versus Dynamic Benefit Measures.- 5.2. The Problem of Endogenous Prices for Local Goods.- 5.3. The Neglect of Consumer Benefits.- 6. Alternative Approaches to Benefit Measurement.- 6.1. The Questionnaire or Sample Survey Approach.- 6.2. Ex Post Accounting…

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Conditional Inference for Restricted Randomization Designs

受限随机化设计的条件推断

In a clinical trial to compare two treatments, suppose that patients are assigned to treatment according to a certain class of restricted randomization rules. Conditional on the difference in numbers between the two treatment groups, the asymptotic null distribution of a class of permutation tests is shown to be Gaussian.

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Strong Embedding of the Estimator of the Distribution Function under Random Censorship

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.…

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On Errors-in-Variables in Binary Regression—Berkson Case

二元回归中的变量测量误差:Berkson情形

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…

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Identification of Binary Response Models

二元反应模型的识别

This article studies identification of the threshold-crossing model of binary response. Most research on binary response has considered specific estimators and tests. The study of identification exposes the foundations of binary response analysis by making explicit the assumptions needed to justify different methods. It also clarifies the connections between reduced-form and structural analyses of binary response data. Assume that the binary outcome z is determined by an…

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Analysis of Repeated Ordered Categorical Outcomes with Possibly Missing Observations and Time-Dependent Covariates

允许缺失观测与时变协变量的重复有序分类结果分析

This article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome. The method, which allows both time-dependent covariates and missing observations, consists of two analytic steps. In the first step, the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by McCullagh (1980).…

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Sensitivity Analysis for Matching with Multiple Controls

多控制匹配的敏感性分析

In observational studies, treated and control subjects may difler in ways that have not been observed, so that reference distributions for statistics that would be appropriate in randomized experiments may lead to incorrect inferences. A previous paper (Rosenbaum, 1987a) proposed a method for displaying the sensitivity of permutation inferences to bias due to an unobserved covariate in two cases: (i) the case of matched pairs, with arbitrary response variables, and (ii) the…

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Conditional Logistic Regression Models for Correlated Binary Data

相关二元数据的条件Logistic回归模型

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…

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Higher-Order Approximations to the Null Distributions of Test Statistics for Nonlinear Restrictions on Regression Coefficients

回归系数非线性约束检验统计量零假设分布的高阶近似

Asymptotic expansions of the distributions of likelihood ratio and Lagrange multiplier test statistics for nonlinear restrictions on regression coefficients are derived under the null hypothesis. Nonlinear restrictions include, as a special case, the identifiability restrictions in the simultaneous equations models. Our analyses of simultaneous equations deal not only with single equations but also subsystems and complete systems. The asymptotic expansions we derive are…

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