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分位数与分布:分位数回归、分布回归、分布效应与随机占优。
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A semiparametric quantile panel data model with an application to estimating the growth effect of FDI

半参数分位数面板模型及外商直接投资增长效应应用

This paper estimates the impact of foreign direct investment on economic growth by proposing a new semiparametric quantile panel data model with correlated random effects, in which some of the coefficients are allowed to depend on some smooth economic variables while other coefficients remain constant. A three-stage estimation procedure is proposed to estimate both constant and functional coefficients and their asymptotic properties are investigated. A simple and easily…

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A quantile correlated random coefficients panel data model

分位数相关随机系数面板数据模型

We propose a generalization of the linear quantile regression model to accommodate possibilities afforded by panel data. Specifically, we extend the correlated random coefficients representation of linear quantile regression (e.g., Koenker, 2005; Section 2.6). We show that panel data allows the econometrician to (i) introduce dependence between the regressors and the random coefficients and (ii) weaken the assumption of comonotonicity across them (i.e., to enrich the…

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Quantile treatment effects in difference in differences models under dependence restrictions and with only two time periods

依赖结构限制下仅有两期数据的双重差分分位数处理效应

This paper shows that the Conditional Quantile Treatment Effect on the Treated is identified under (i) a Conditional Distributional Difference in Differences assumption and (ii) a new assumption that the dependence (the copula) between the change in untreated potential outcomes and the initial level of untreated potential outcomes is the same for the treated group and untreated group. We consider estimation and inference with discrete covariates and propose a uniform…

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TESTING FOR A GENERAL CLASS OF FUNCTIONAL INEQUALITIES

一般函数不等式的检验

In this article, we propose a general method for testing inequality restrictions on nonparametric functions. Our framework includes many nonparametric testing problems in a unified framework, with a number of possible applications in auction models, game theoretic models, wage inequality, and revealed preferences. Our test involves a one-sided version of L p functionals of kernel-type estimators (1 ≤ p < ∞ ) and is easy to implement in general, mainly due to its recourse to…

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Semiparametrically Efficient Estimation in Quantile Regression of Secondary Analysis

病例对照研究次要结局分位数回归的半参数有效估计

Summary Analysing secondary outcomes is a common practice for case–control studies. Traditional secondary analysis employs either completely parametric models or conditional mean regression models to link the secondary outcome to covariates. In many situations, quantile regression models complement mean-based analyses and provide alternative new insights on the associations of interest. For example, biomedical outcomes are often highly asymmetric, and median regression is…

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Portfolio optimization based on stochastic dominance and empirical likelihood

基于随机占优与经验似然的投资组合优化

This study develops a portfolio optimization method based on the Stochastic Dominance (SD) decision criterion and the Empirical Likelihood (EL) estimation method. SD and EL share a distribution-free assumption framework which allows for dynamic and non-Gaussian multivariate return distributions. The SD/EL method can be implemented using a two-stage procedure which first elicits the implied probabilities using Convex Optimization and subsequently constructs the optimal…

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Comparing distributions by multiple testing across quantiles or CDF values

通过跨分位数或累积分布函数值的多重检验比较分布

We first show that one-sample and two-sample Kolmogorov–Smirnov tests may be interpreted as multiple testing procedures, nonparametrically testing equality at each point in the distribution with strong control of the finite-sample familywise error rate. Second, we provide an alternative procedure that distributes power across the distribution more evenly than the Kolmogorov–Smirnov test, which suffers low sensitivity to tail deviations. Third, we provide a formula for…

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Partial identification and inference in censored quantile regression

删失分位数回归的部分识别与推断

In this paper, we study partial identification and inference in a linear quantile regression, where the dependent variable is subject to possibly unknown dependent censoring characterized by an Archimedean copula. An outer set of the identified set for the regression coefficient is characterized via inequality constraints. For one-parameter ordered families of Archimedean copulas, we construct a simple confidence set by inverting an asymptotically pivotal statistic. A…

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Current status linear regression

We construct $\sqrt{n}$-consistent and asymptotically normal estimates for the finite dimensional regression parameter in the current status linear regression model, which do not require any smoothing device and are based on maximum likelihood estimates (MLEs) of the infinite dimensional parameter. We also construct estimates, again only based on these MLEs, which are arbitrarily close to efficient estimates, if the generalized Fisher information is finite. This type of…

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Exact and higher-order properties of the MLE in spatial autoregressive models, with applications to inference

空间自回归模型中极大似然估计量的精确与高阶性质及推断应用

The quasi-maximum likelihood estimator for the autoregressive parameter in a spatial autoregression usually cannot be written explicitly in terms of the data. A rigorous analysis of the first-order asymptotic properties of the estimator, under some assumptions on the evolution of the spatial design matrix, is available in Lee (2004), but very little is known about its exact or higher-order properties. In this paper we first show that the exact cumulative distribution…

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Modeling Persistent Trends in Distributions

分布中持续趋势的建模

We present a nonparametric framework to model a short sequence of probability distributions that vary both due to underlying effects of sequential progression and confounding noise. To distinguish between these two types of variation and estimate the sequential-progression effects, our approach leverages an assumption that these effects follow a persistent trend. This work is motivated by the recent rise of single-cell RNA-sequencing experiments over a brief time course,…

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Oracle Estimation of a Change Point in High-Dimensional Quantile Regression

高维分位数回归中变点的预言式估计

In this paper, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop $\ell_1$-penalized estimators of both regression coefficients and the threshold parameter. Our penalized estimators not only select covariates but also discriminate between a model with homogeneous sparsity and a model with a change point. As a result, it is not necessary to know or pretest whether the change point is…

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Quantile-Optimal Treatment Regimes

分位数最优治疗规则

Finding the optimal treatment regime (or a series of sequential treatment regimes) based on individual characteristics has important applications in areas such as precision medicine, government policies and active labor market interventions. In the current literature, the optimal treatment regime is usually defined as the one that maximizes the average benefit in the potential population. This paper studies a general framework for estimating the quantile-optimal treatment…

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Estimation and Inference of Heterogeneous Treatment Effects using Random Forests

利用随机森林估计异质性处理效应并进行统计推断

Many scientific and engineering challenges -- ranging from personalized medicine to customized marketing recommendations -- require an understanding of treatment effect heterogeneity. In this paper, we develop a non-parametric causal forest for estimating heterogeneous treatment effects that extends Breiman's widely used random forest algorithm. In the potential outcomes framework with unconfoundedness, we show that causal forests are pointwise consistent for the true…

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Eliciting Subjective Survival Curves: Lessons from Partial Identification

主观生存曲线的获取:部分识别的启示

When analyzing data on subjective expectations of continuous outcomes, researchers have access to a limited number of reported probabilities for each respondent from which to construct complete distribution functions. Moreover, reported probabilities may be rounded and thus not equal to true beliefs. Using survival expectations elicited from a representative sample from the Netherlands, we investigate what can be learned if we take these two sources of missing information…

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Practical Kolmogorov–Smirnov Testing by Minimum Distance Applied to Measure Top Income Shares in Korea

基于最小距离的实用 Kolmogorov–Smirnov 检验:韩国顶端收入份额的应用

We study Kolmogorov–Smirnov goodness-of-fit tests for evaluating distributional hypotheses where unknown parameters need to be fitted. Following the work of Pollard (1980), our approach uses a Cramér–von Mises minimum distance estimator for parameter estimation. The asymptotic null distribution of the resulting test statistic is represented by invariance principle arguments as a functional of a Brownian bridge in a simple regression format for which asymptotic critical…

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A Unified Approach to Estimating and Testing Income Distributions With Grouped Data

分组数据下收入分布估计与检验的统一方法

We propose a unified approach that is flexibly applicable to various types of grouped data for estimating and testing parametric income distributions. To simplify the use of our approach, we also provide a parametric bootstrap method and show its asymptotic validity. We also compare this approach with existing methods for grouped income data, and assess their finite-sample performance by a Monte Carlo simulation. For empirical demonstrations, we apply our approach to…

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Gradient-based structural change detection for nonstationary time series M-estimation

非平稳时间序列 M 估计中的梯度结构变化检测

We consider structural change testing for a wide class of time series M-estimation with nonstationary predictors and errors. Flexible predictor-error relationships, including exogenous, state-heteroscedastic and autoregressive regressions and their mixtures, are allowed. New uniform Bahadur representations are established with nearly optimal approximation rates. A CUSUM-type test statistic based on the gradient vectors of the regression is considered. In this paper, a simple…

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A smooth block bootstrap for quantile regression with time series

时间序列分位数回归的平滑分块自助法

Quantile regression allows for broad (conditional) characterizations of a response distribution beyond conditional means and is of increasing interest in economic and financial applications. Because quantile regression estimators have complex limiting distributions, several bootstrap methods for the independent data setting have been proposed, many of which involve smoothing steps to improve bootstrap approximations. Currently, no similar advances in smoothed bootstraps…

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Non‐parametric inference on (conditional) quantile differences and interquantile ranges, using L‐statistics

利用 L 统计量对(条件)分位数差与分位距进行非参数推断

We provide novel, high‐order accurate methods for non‐parametric inference on quantile differences between two populations in both unconditional and conditional settings. These quantile differences correspond to (conditional) quantile treatment effects under (conditional) independence of a binary treatment and potential outcomes. Our methods use the probability integral transform and a Dirichlet (rather than Gaussian) reference distribution to pick appropriate L‐statistics…

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Exact computation of GMM estimators for instrumental variable quantile regression models

工具变量分位数回归模型中GMM估计量的精确计算

Summary We show that the generalized method of moments (GMM) estimation problem in instrumental variable quantile regression (IVQR) models can be equivalently formulated as a mixed‐integer quadratic programming problem. This enables exact computation of the GMM estimators for the IVQR models. We illustrate the usefulness of our algorithm via Monte Carlo experiments and an application to demand for fish.

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Nonparametric Welfare and Demand Analysis with Unobserved Individual Heterogeneity

存在不可观测个体异质性时的非参数福利与需求分析

This paper combines revealed preference and nonparametric estimation techniques to obtain nonparametric bounds on the distribution of the money metric utility and demand functions over a population of heterogeneous households. Our approach is independent of any functional specification on the household utility functions. Our method applies the weak axiom of revealed preference to a population of heterogeneous households. Although this does not produce the sharpest bounds, we…

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Single-Index-Based CoVaR With Very High-Dimensional Covariates

超高维协变量下基于单指标模型的 CoVaR

Systemic risk analysis reveals the interdependencies of risk factors especially in tail event situations. In applications the focus of interest is on capturing joint tail behavior rather than a variation around the mean. Quantile and expectile regression are used here as tools of data analysis. When it comes to characterizing tail event curves one faces a dimensionality problem, which is important for CoVaR (Conditional Value at Risk) determination. A projection-based…

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A Simple Adjustment for Bandwidth Snooping

带宽窥探的简单校正

Kernel-based estimators such as local polynomial estimators in regression discontinuity designs are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the bandwidth based on this analysis, the associated confidence intervals (CIs) may not have correct coverage, even if the estimator is unbiased. This article proposes a simple adjustment that gives correct coverage in such situations: replace the…

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