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Nonparametric estimation of an additive model with a link function

具有连接函数的加性模型非参数估计

This paper describes an estimator of the additive components of a nonparametric additive model with a known link function. When the additive components are twice continuously differentiable, the estimator is asymptotically normally distributed with a rate of convergence in probability of n−2/5. This is true regardless of the (finite) dimension of the explanatory variable. Thus, in contrast to the existing asymptotically normal estimator, the new estimator has no curse of…

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Semiparametric estimation of a panel data proportional hazards model with fixed effects

带固定效应的面板比例风险模型的半参数估计

This paper considers a panel duration model that has a proportional hazards specification with fixed effects. The paper shows how to estimate the baseline and integrated baseline hazard functions without assuming that they belong to known, finitedimensional families of functions. Existing estimators assume that the baseline hazard function belongs to a known parametric family. Therefore, the estimators presented here are more general than existing ones. This paper also…

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Bootstrap Methods for Markov Processes

马尔可夫过程的自助重抽样方法

The block bootstrap is the best known bootstrap method for time-series data when the analyst does not have a parametric model that reduces the data generation process to simple random sampling. However, the errors made by the block bootstrap converge to zero only slightly faster than those made by first-order asymptotic approximations. This paper describes a bootstrap procedure for data that are generated by a Markov process or a process that can be approximated by a Markov…

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An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model Against a Nonparametric Alternative

针对非参数备择的参数均值回归模型自适应、速率最优检验

We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the fastest possible rate. This rate is slower than n[superscript -1/2]. Some existing tests have nontrivial power against restricted classes of alternatives whose distance from the…

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Nonparametric Analysis of Randomized Experiments with Missing Covariate and Outcome Data

协变量和结局缺失的随机实验非参数分析

Analysis of randomized experiments with missing covariate and outcome data is problematic, because the population parameters of interest are not identified unless one makes untestable assumptions about the distribution of the missing data. This article shows how population parameters can be bounded without making untestable distributional assumptions. Bounds are also derived under the assumption that covariate data are missing completely at random. In each case the bounds…

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Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity

含未观测异质性的比例风险模型半参数估计

The proportional hazard model with unobserved heterogeneity gives the hazard function of a random variable conditional on covariates and a second random variable representing unobserved heterogeneity. This paper shows how to estimate the baseline hazard function and the distribution of the unobserved heterogeneity nonparametrically. The baseline hazard function and heterogeneity distribution are assumed to satisfy smoothness conditions but are not assumed to belong to known,…

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Bootstrap Methods for Median Regression Models

中位数回归模型的自助法

The least-absolute-deviations (LAD) estimator for a median-regression or censored median-regression model does not satisfy the standard conditions for obtaining asymptotic refinements through use of the bootstrap because the LAD objective function is not smooth. This paper overcomes this problem by smoothing the objective function. The smoothed estimator is asymptotically equivalent to the ordinary LAD estimator. With bootstrap critical values, the rejection probabilities of…

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Direct Semiparametric Estimation of Single-Index Models with Discrete Covariates

含离散协变量单指标模型的直接半参数估计

Others have developed average derivative estimators of the parameter β in the model E(Y|X = x) = G(xβ), where G is an unknown function and X is a random vector. These estimators are noniterative and easy to compute but require that X be continuously distributed. This article develops a noniterative, easily computed estimator of β for models in which some components of X are discrete. The estimator is n ½ consistent and asymptotically normal. An application to data on product…

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Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators

基于广义矩估计量的检验的自助法临界值

Tests based on generalized-method-of-moments estimators often have true levels that differ greatly from their nominal levels when asymptotic critical values are used. This paper gives conditions under which the bootstrap provides asymptotic refinements to the critical values of t tests and the test of overidentifying restrictions. Particular attention is given to the case of dependent data. It is shown that, with such data, the bootstrap must sample blocks of data and that…

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Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable

因变量未知变换回归模型的半参数估计

This paper shows how to estimate a model in which an unknown transformation of the dependent variable is a linear function of explanatory variables plus an unobserved random variable, U, whose distribution is unknown. The model nests many familiar parametric and semiparametric models, including models with Box-Cox transformed dependent variables and proportional hazards models with and without unobserved heterogeneity. The paper develops root-n consistent, asymptotically…

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Semiparametric Estimation of Regression Models for Panel Data

面板数据回归模型的半参数估计

Linear models with error components are widely used to analyse panel data. Some applications of these models require knowledge of the probability densities of the error components. Existing methods handle this requirement by assuming that the densities belong to known parametric families of distributions (typically the normal distribution). This paper shows how to carry out nonparametric estimation of the densities of the error components, thereby avoiding the assumption…

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Identification and Robustness with Contaminated and Corrupted Data

数据污染与损坏下的识别及稳健性

Robust estimation aims at developing point estimators that are not highly sensitive to errors in data. However, the population parameters of interest are not identified under the assumptions of robust estimation, so the rationale for point estimation is not apparent. This paper shows that, under error models used in robust estimation, unidentified population parameters can often be bounded. The bounds provide information that is not available in robust estimation. For…

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On blocking rules for the bootstrap with dependent data

依赖数据自助法的分块选择规则

SUMMARY: We address the issue of optimal block choice in applications of the block bootstrap to dependent data. It is shown that optimal block size depends significantly on context, being equal to n1/3, n1/4 and n1/5 in the cases of variance or bias estimation, estimation of a onesided distribution function, and estimation of a two-sided distribution function, respectively. A clear intuitive explanation of this phenomenon is given, together with outlines of theoretical…

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Testing a Parametric Model Against a Semiparametric Alternative

针对半参数备择检验参数模型

This paper describes a method for testing a parametric model of the mean of a random variable Y conditional on a vector of explanatory variables X against a semiparametric alternative. The test is motivated by a conditional moment test against a parametric alternative and amounts to replacing the parametric alternative model with a semiparametric model. The resulting semiparametric test is consistent against a larger set of alternatives than are parametric conditional…

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Optimal Rates of Convergence of Parameter Estimators in the Binary Response Model with Weak Distributional Assumptions

弱分布假设下二元响应模型参数估计的最优收敛速度

The smoothed maximum score estimator of the coefficient vector of a binary response model is consistent and, after centering and suitable normalization, asymptotically normally distributed under weak assumptions [5]. Its rate of convergence in probability is N − h /(2 h +1) , where h ≥ 2 is an integer whose value depends on the strength of certain smoothness assumptions. This rate of convergence is faster than that of the maximum score estimator of Manski [11,12], which…

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A Smoothed Maximum Score Estimator for the Binary Response Model

二元响应模型的平滑最大得分估计量

This paper describes a semiparametric estimator for binary response models in which there may be arbitrary heteroskedasticity of unknown form. The estimator is obtained by maximizing a smoothed version of the objective function of C. Manski's maximum score estimator. The smoothing procedure is similar to that used in kernel nonparametric density estimation. The resulting estimator's rate of convergence in probability is the fastest possible under the assumptions that are…

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The role of the list price in housing markets: Theory and an econometric model

住房市场中挂牌价的作用:理论与计量模型

Abstract Houses are routinely sold at prices below, but rarely sold at prices above, their list prices. List prices appear to be price ceilings that preclude the possibility of sales at higher prices. This paper presents a theory of sellers' behaviour that explains why there are list prices in housing markets and why list prices are distinct from sellers' reservation prices. The theory forms the basis of an econometric model that has been estimated using data from the…

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