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Estimation and Inference With Weak, Semi-Strong, and Strong Identification

弱、半强与强识别下的估计和推断

This paper analyzes the properties of standard estimators, tests, and confidence sets (CS's) for parameters that are unidentified or weakly identified in some parts of the parameter space. The paper also introduces methods to make the tests and CS's robust to such identification problems. The results apply to a class of extremum estimators and corresponding tests and CS's that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions…

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Nonparametric Instrumental Variable Estimation of Structural Quantile Effects

结构分位数效应的非参数工具变量估计

We study the asymptotic distribution of Tikhonov Regularized estimation of quantile structural effects implied by a nonseparable model. The nonparametric instrumental variable estimator is based on a minimum distance principle. We show that the minimum distance problem without regularization is locally ill-posed, and consider penalization by the norms of the parameter and its derivatives. We derive pointwise asymptotic normality and develop a consistent estimator of the…

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Impossibility Results for Nondifferentiable Functionals

不可微泛函的不可能性结果

We examine challenges to estimation and inference when the objects of interest are nondifferentiable functionals of the underlying data distribution. This situation arises in a number of applications of bounds analysis and moment inequality models, and in recent work on estimating optimal dynamic treatment regimes. Drawing on earlier work relating differentiability to the existence of unbiased and regular estimators, we show that if the target object is not differentiable in…

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Functional Differencing

函数差分法

In nonlinear panel data models, the incidental parameter problem remains a challenge to econometricians. Available solutions are often based on ingenious, model-specific methods. In this paper, we propose a systematic approach to construct moment restrictions on common parameters that are free from the individual fixed effects. This is done by an orthogonal projection that differences out the unknown distribution function of individual effects. Our method applies generally…

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Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals

广义残差可能不光滑的非参数条件矩模型估计

This paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators, which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the…

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Wild bootstrap for quantile regression

分位数回归的野生自助法

The existing theory of the wild bootstrap has focused on linear estimators. In this note, we broaden its validity by providing a class of weight distributions that is asymptotically valid for quantile regression estimators. As most weight distributions in the literature lead to biased variance estimates for nonlinear estimators of linear regression, we propose a modification of the wild bootstrap that admits a broader class of weight distributions for quantile regression. A…

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Empirical likelihood and quantile regression in longitudinal data analysis

纵向数据分析中的经验似然与分位数回归

We propose a novel quantile regression approach for longitudinal data analysis which naturally incorporates auxiliary information from the conditional mean model to account for within-subject correlations. The efficiency gain is quantified theoretically and demonstrated empirically via simulation studies and the analysis of a real dataset.

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A sieve M-theorem for bundled parameters in semiparametric models, with application to the efficient estimation in a linear model for censored data

半参数模型中捆绑参数的筛 M 定理及其删失线性模型有效估计应用

In many semiparametric models that are parameterized by two types of parameters - a Euclidean parameter of interest and an infinite-dimensional nuisance parameter, the two parameters are bundled together, i.e., the nuisance parameter is an unknown function that contains the parameter of interest as part of its argument. For example, in a linear regression model for censored survival data, the unspecified error distribution function involves the regression coefficients.…

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Maximum Likelihood Estimations and EM Algorithms With Length-Biased Data

长度偏倚数据的最大似然估计与 EM 算法

Length-biased sampling has been well recognized in economics, industrial reliability, etiology applications, epidemiological, genetic and cancer screening studies. Length-biased right-censored data have a unique data structure different from traditional survival data. The nonparametric and semiparametric estimations and inference methods for traditional survival data are not directly applicable for length-biased right-censored data. We propose new expectation-maximization…

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Semiparametric Approach to a Random Effects Quantile Regression Model

随机效应分位数回归模型的半参数方法

We consider a random effects quantile regression analysis of clustered data and propose a semiparametric approach using empirical likelihood. The random regression coefficients are assumed independent with a common mean, following parametrically specified distributions. The common mean corresponds to the population-average effects of explanatory variables on the conditional quantile of interest, while the random coefficients represent cluster specific deviations in the…

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On finite sample properties of alternative estimators of coefficients in a structural equation with many instruments

多工具变量结构方程系数估计量的有限样本比较

We compare four different estimation methods for the coefficients of a linear structural equation with instrumental variables. As the classical methods we consider the limited information maximum likelihood (LIML) estimator and the two-stage least squares (TSLS) estimator, and as the semi-parametric estimation methods we consider the maximum empirical likelihood (MEL) estimator and the generalized method of moments (GMM) (or the estimating equation) estimator. Tables and…

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A nonparametric analysis of black-white differences in intergenerational income mobility in the United States

美国黑人与白人代际收入流动差异的非参数分析

Lower intergenerational income mobility for blacks is a likely cause behind the persistent interracial gap in economic status in the United States.However, few studies have analyzed black-white differences in intergenerational income mobility and the factors that determine these differences.This is largely due to the absence of appropriate methodological tools.We develop nonparametric methods to estimate the effects of covariates on two measures of mobility.We first consider…

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On deconvolution of distribution functions

分布函数的反卷积估计

The subject of this paper is the problem of nonparametric estimation of a continuous distribution function from observations with measurement errors. We study minimax complexity of this problem when unknown distribution has a density belonging to the Sobolev class, and the error density is ordinary smooth. We develop rate optimal estimators based on direct inversion of empirical characteristic function. We also derive minimax affine estimators of the distribution function…

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A simple approach to quantile regression for panel data

This paper provides a set of sufficient conditions that point identify a quantile regression model with fixed effects. It also proposes a simple transformation of the data that gets rid of the fixed effects under the assumption that these effects are location shifters. The new estimator is consistent and asymptotically normal as both n and T grow.

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Bayesian Time-Varying Quantile Forecasting for Value-at-Risk in Financial Markets

用于金融市场风险价值预测的贝叶斯时变分位数模型

Recently, advances in time-varying quantile modeling have proven effective in financial Value-at-Risk forecasting. Some well-known dynamic conditional autoregressive quantile models are generalized to a fully nonlinear family. The Bayesian solution to the general quantile regression problem, via the Skewed-Laplace distribution, is adapted and designed for parameter estimation in this model family via an adaptive Markov chain Monte Carlo sampling scheme. A simulation study…

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Bayesian isotonic density regression

贝叶斯保序密度回归

Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not clear whether such priors have full support so that any true data-generating model…

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Quantile regression for dynamic panel data with fixed effects

带固定效应的动态面板分位数回归

This paper studies a quantile regression dynamic panel model with fixed effects. Panel data fixed effects estimators are typically biased in the presence of lagged dependent variables as regressors. To reduce the dynamic bias, we suggest the use of the instrumental variables quantile regression method of Chernozhukov and Hansen (2006) along with lagged regressors as instruments. In addition, we describe how to employ the estimated models for prediction. Monte Carlo…

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A Simple Correction to Remove the Bias of the Gini Coefficient due to Grouping

消除分组导致的基尼系数偏差的简单修正

We propose a first-order bias correction term for the Gini index to reduce the bias due to grouping. It depends on only the number of individuals in each group and is derived from a measurement error framework. We also provide a formula for the remaining second-order bias. Both Monte Carlo and EU and U.S. empirical evidence show that the first-order correction reduces a considerable share of the bias, but that some remaining second-order bias is increasing in the variance.…

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Non-parametric bounds on quantiles under monotonicity assumptions: with an application to the Italian education returns

单调性假设下分位数的非参数界:意大利教育回报应用

Within the inferential context of predicting a distribution of potential outcomes P[y(t)] under a uniform treatment assignment t ∈ T, this paper deals with partial identification of the α-quantile of the distribution of interest Qα[y(t)] under relatively weak and credible monotonicity-type assumptions on the individual response functions and the population selection process. On the theoretical side, the paper adds to the existing results on non-parametric bounds on quantiles…

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Test statistics for prospect and Markowitz stochastic dominances with applications

前景随机占优与马科维茨随机占优的检验统计量及应用

Levy and Levy (2002, 2004) extend the stochastic dominance (SD) theory for risk averters and risk seekers by developing the prospect SD (PSD) and Markowitz SD (MSD) theory for investors with S‐shaped and reverse S‐shaped (RS‐shaped) utility functions, respectively. Davidson and Duclos (2000) develop SD tests for risk averters whereas Sriboonchitra et al. (2009) modify their statistics to obtain SD tests for risk seekers. In this paper, we extend their work by developing new…

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Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules

利用阈值加权与分位数加权评分规则比较密度预测

We propose a method for comparing density forecasts that is based on weighted versions of the continuous ranked probability score. The weighting emphasizes regions of interest, such as the tails or the center of a variable’s range, while retaining propriety, as opposed to a recently developed weighted likelihood ratio test, which can be hedged. Threshold- and quantile-based decompositions of the continuous ranked probability score can be illustrated graphically and provide…

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On balanced random imputation in surveys

调查中的平衡随机插补

Random imputation methods are often used in practice because they tend to preserve the distribution of the variable being imputed, which is an important property when the goal is to estimate population quantiles. However, this type of imputation method introduces additional variability, the imputation variance, due to the random selection of residuals. In this paper, we propose a class of random balanced imputation methods under which the imputation variance is eliminated…

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Non-Parametric Bayesian Inference on Bivariate Extremes

二元极值的非参数贝叶斯推断

Summary The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme value distribution may be approximated by that of its extreme value attractor. The extreme value attractor has margins that belong to a three-parameter family and a dependence structure which is characterized by a probability measure on the unit interval with mean equal to 12, which is called the spectral measure. Inference is done in a Bayesian framework using a censored…

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Penalized Composite Quasi-Likelihood for Ultrahigh Dimensional Variable Selection

用于超高维变量选择的惩罚复合准似然

Summary In high dimensional model selection problems, penalized least square approaches have been extensively used. The paper addresses the question of both robustness and efficiency of penalized model selection methods and proposes a data-driven weighted linear combination of convex loss functions, together with weighted L1-penalty. It is completely data adaptive and does not require prior knowledge of the error distribution. The weighted L1-penalty is used both to ensure…

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