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A Generalized Moments Specification Test of the Proportional Hazards Model

比例风险模型的广义矩设定检验

This article describes a generalized moments specification test of the semiparametric proportional hazards model of Cox. In contrast to other specification tests for this model, the generalized moments test is applicable in the presence of continuous explanatory variables and does not require assigning the data to predetermined cells. The results of a Monte Carlo investigation suggest that the generalized moments test has good finite-sample properties and that it is more…

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Semiparametic Nonlinear Least-Squares Estimation of Truncated Regression Models

截断回归模型的半参数非线性最小二乘估计

This article provides a semiparametric method for the estimation of truncated regression models where the disturbances are independent of the regressors before truncation. This independence property provides useful information on model identification and estimation. Our estimate is shown to be -consistent and asymptotically normal. A consistent estimate of the asymptotic covariance matrix of the estimator is provided. Monte Carlo experiments are performed to investigate some…

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Time aggregation and the distributional shape of unemployment duration

时间聚合与失业持续期的分布形态

Abstract This paper reports empirical evidence on the sensitivity of unemployment duration regression estimates to distributional assumptions and to time aggregation. The results indicate that parameter estimates are robust to distributional assumptions, while estimates of duration dependence are not. Time aggregation does not seem to have drastic effects on the estimates in a simple parametric model like the Weibull, but can produce dramatic changes in the more complicated…

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A mixture model combining logistic regression with proportional hazards regression

结合逻辑回归与比例风险回归的混合模型

A model is proposed for the analysis of censored data which combines a logistic formulation for the probability of occurrence of an event with a proportional hazards specification for the time of occurrence of the event. The proposed model is a semiparametric generalization of a parametric model due to Farewell (1982). Estimates of the regression parameters are obtained by maximizing a Monte Carlo approximation of a marginal likelihood and the EM algorithm is used to…

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Inference using surrogate outcome data and a validation sample

利用替代结局数据与验证样本进行推断

In the context of estimating β from the regression model Pβ(Y|X), relating response Y to covariates X, suppose that only a surrogate response S is available for most study subjects. Suppose that for a random subsample of the study cohort, termed the validation sample, the true outcome Y is available in addition to S. We consider maximum likelihood estimation of β from such data and show that it is nonrobust to misspecification of the distribution relating the surrogate to…

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Estimation of the time-dependent accelerated failure time model in the presence of confounding factors

存在混杂因素时的时变加速失效时间模型估计

Cox & Oakes (1984, p. 66) introduced the ‘strong version’ of the accelerated failure time model with time-dependent exposures. We provide conditions under which this model could be used to estimate, from observational data, the causal effect of a time-varying exposure or treatment on time to an event of interest in the presence of time-dependent confounding variables. We propose a class of semiparametric tests and estimators for the model parameters. This class contains an…

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Semiparametric estimation of an accelerated failure time model with time-dependent covariates

含时变协变量的加速失效时间模型的半参数估计

A class of semiparametric accelerated failure time models is introduced that are useful for modelling the relationship of survival distributions to time dependent covariates. A class of semiparametric rank estimators is derived for the parameters in this model when the survival data are right censored. These estimates are shown to be consistent, and asymptotically normal with variances that can be consistently estimated. It is also shown that estimators within this class…

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A projected likelihood function for semiparametric models

半参数模型的投影似然函数

In a sequence of papers, McLeish (1984), Hutton & Nelson (1986) and Godambe & Heyde (1987) have motivated the use of the quasi-score function as an estimating function for semiparametric models by showing that it is the projection of the true score into a class of unbiased estimating functions. Thus the quasi-score approximates the score within this class of functions. In this paper, we introduce a class of inference functions for independent observations that contain…

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Semiparametric ARCH Models

半参数 ARCH 模型

A semiparametric ARCH model is introduced with conditional first and second moments given by ARMA and ARCH formulations, and a conditional density that is approximated by a nonparametric density estimator. For several densities, the relative efficiency of the quasi-maximum likelihood estimator is compared with maximum likelihood under correct specification. These potential efficiency gains for a fully adaptive procedure are compared in a Monte Carlo experiment with the…

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Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models

半参数与非参数模型的自动频域推断

The author considers frequency domain time series analysis, where smoothing in nonparametric spectrum estimation is data-dependent. Uniform convergence of spectrum estimates is established and applied to a semiparametric model, parameterized over possibly only a subset of the frequencies, in which disturbances have nonparametric autocorrelation. Optimal instruments depend on the disturbance spectrum and frequency response function, which is nonparametric in incomplete…

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Semiparametric Estimation of Monotone and Concave Utility Functions for Polychotomous Choice Models

多类别离散选择模型中单调凹效用函数的半参数估计

This paper introduces a semiparametric estimation method for Polychotomous Choice models. The method does not require a parametric structure for the systematic subutility of observable exogenous variables. The distribution of the random terms is assumed to be known up to a finite-dimensional parameter vector. In contrast, previous semiparametric methods of estimating discrete choice models have concentrated on relaxing parametric subutility parametrically specified. The…

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Semiparametric Estimation in Logistic Measurement Error Models

Logistic 测量误差模型的半参数估计

SUMMARY We describe semiparametric estimation and inference in a logistic regression model with measurement error in the predictors. The particular measurement error model consists of a primary data set in which only the response Y and a fallible surrogate W of the true predictor X are observed, plus a smaller validation data set for which (Y, X, W) are observed. Except for the underlying assumption of a logistic model in the true predictor, no parametric distributional…

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On Maximum Likelihood Estimation in Infinite Dimensional Parameter Spaces

无限维参数空间中的最大似然估计

An approximate maximum likelihood estimate is known to be consistent under some compactness and integrability conditions. In this paper we study its convergence rate and its asymptotic efficiency in estimating smooth functionals of the parameter. We provide conditions under which the rate of convergence can be established. This rate is essentially governed by the size of the space of score functions as measured by an entropy index. We also show that, for a large class of…

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Some Monte Carlo Evidence on the Relative Efficiency of Parametric and Semiparametric EGLS Estimators

One of the most common practical problems in statistics and econometrics is the estimation of linear regression models with heteroscedastic errors. This article reports the results of a Monte Carlo comparison of various parametric and semiparametric estimated generalized least squares (EGLS) estimators. In small-sized (20) and sometimes medium-sized (50) samples, ordinary least squares dominated the other techniques for low levels of heteroscedasticity. In medium-sized…

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Review Papers: Recent Developments in Nonparametric Density Estimation

综述:非参数密度估计的近期发展

Advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research, and especially the development of nonparametric data analysis procedures. In particular, theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics, such as nonparametric regression, nonparametric discrimination, and nonparametric pattern recognition. This…

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Semiparametric Estimation in the Rasch Model and Related Exponential Response Models, Including a Simple Latent Class Model for Item Analysis

Rasch及相关指数响应模型的半参数估计与潜类别分析

The Rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects, leading to the failure of the usual likelihood methodology. Both conditional-likelihood methods and mixture-model techniques have been used to circumvent these problems. In this article, we show that these seemingly unrelated analyses are in fact closely linked to each other, despite dramatic…

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Recent Developments in Nonparametric Density Estimation

非参数密度估计的近期发展

Advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research, and especially the development of nonparametric data analysis procedures. In particular, theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics, such as nonparametric regression, nonparametric discrimination, and nonparametric pattern recognition. This…

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Orthogonality of Estimating Functions and Nuisance Parameters

估计函数的正交性与干扰参数

Cox & Reid (1987) proposed the technique of orthogonalizing parameters, to deal with the general problem of nuisance parameters, within fully parametric models. They obtained a large-sample approximation to the conditional likelihood. Along the same lines Davison (1988) studied generalized linear models. In the present paper we deal with the problem of nuisance parameters, within a semiparametric setup which includes the class of distributions associated with generalized…

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Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models

非参数与半参数回归模型中级数估计量的渐近正态性

This paper establishes the asymptotic normality of series estimators for nonparametric regression models. Gallant's Fourier flexible form estimators, trigonometric series estimators, and polynomial series estimators are prime examples of the estimators covered by the results. The results apply to a wide variety of estimates in the regression model under consideration, including derivatives and integrals of the regression function. The errors in the model may be homoskedastic…

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Testing for Preference Change in Consumer Demand: An Indirectly Separable, Semiparametric Model

消费者需求中的偏好变化检验:间接可分的半参数模型

This article considers the hypothesis that preference changes may partly explain observed consumption patterns. A model is developed based on indirect weak separability. The kernel estimator of the regression function models the unknown shape of demad functions, and a parametric structure models seasonality, dynamics, and preference change. This semiparametric specification is applied to U.S. meat demand. The results support the notion that changes in consumer preferences,…

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