Econometric Theory最新文献

英文中文

A MOLLIFIER APPROACH TO THE DECONVOLUTION OF PROBABILITY DENSITIES 概率密度反褶积的一种软化方法

IF 0.8 4区经济学 Q3 ECONOMICS

Econometric Theory

Pub Date : 2022-10-28 DOI: 10.1017/s0266466622000457

P. Maréchal, L. Simar, A. Vanhems

We use mollification to regularize the problem of deconvolution of random variables. This regularization method offers a unifying and generalizing framework in order to compare the benefits of various filter-type techniques like deconvolution kernels, Tikhonov, or spectral cutoff methods. In particular, the mollifier approach allows to relax some restrictive assumptions required for the deconvolution kernels, and has better stabilizing properties compared with spectral cutoff or Tikhonov. We show that this approach achieves optimal rates of convergence for both finitely and infinitely smoothing convolution operators under Besov and Sobolev smoothness assumptions on the unknown probability density. The qualification can be arbitrarily high depending on the choice of the mollifier function. We propose an adaptive choice of the regularization parameter using the Lepskiĭ method, and we provide simulations to compare the finite sample properties of our estimator with respect to the well-known regularization methods.

我们使用软化来正则化随机变量的反褶积问题。这种正则化方法提供了一个统一和推广的框架，以便比较各种滤波器类型技术的优点，如去卷积核、Tikhonov或谱截止方法。特别是，软化器方法允许放松反褶积核所需的一些限制性假设，并且与谱截止或Tikhonov相比具有更好的稳定性。我们证明，在未知概率密度的Besov和Sobolev光滑假设下，该方法对有限和无限光滑卷积算子都实现了最优收敛速度。根据软化剂功能的选择，资格可以任意高。我们使用Lepskiĭ方法提出了正则化参数的自适应选择，并提供了仿真，以将我们的估计器的有限样本特性与众所周知的正则化方法进行比较。

引用次数: 1

ANALYSIS OF GLOBAL AND LOCAL OPTIMA OF REGULARIZED QUANTILE REGRESSION IN HIGH DIMENSIONS: A SUBGRADIENT APPROACH 高维正则分位数回归的全局和局部最优分析：一种次梯度方法

IF 0.8 4区经济学 Q3 ECONOMICS

Econometric Theory

Pub Date : 2022-10-18 DOI: 10.1017/s0266466622000421

Lan Wang, Xuming He

Regularized quantile regression (QR) is a useful technique for analyzing heterogeneous data under potentially heavy-tailed error contamination in high dimensions. This paper provides a new analysis of the estimation/prediction error bounds of the global solution of $L_1$ -regularized QR (QR-LASSO) and the local solutions of nonconvex regularized QR (QR-NCP) when the number of covariates is greater than the sample size. Our results build upon and significantly generalize the earlier work in the literature. For certain heavy-tailed error distributions and a general class of design matrices, the least-squares-based LASSO cannot achieve the near-oracle rate derived under the normality assumption no matter the choice of the tuning parameter. In contrast, we establish that QR-LASSO achieves the near-oracle estimation error rate for a broad class of models under conditions weaker than those in the literature. For QR-NCP, we establish the novel results that all local optima within a feasible region have desirable estimation accuracy. Our analysis applies to not just the hard sparsity setting commonly used in the literature, but also to the soft sparsity setting which permits many small coefficients. Our approach relies on a unified characterization of the global/local solutions of regularized QR via subgradients using a generalized Karush–Kuhn–Tucker condition. The theory of the paper establishes a key property of the subdifferential of the quantile loss function in high dimensions, which is of independent interest for analyzing other high-dimensional nonsmooth problems.

正则分位数回归（QR）是一种在高维潜在重尾误差污染下分析异质数据的有用技术。当协变量数大于样本量时，本文对$L_1$-正则化QR（QR-LASSO）的全局解和非凸正则化QR的局部解的估计/预测误差界进行了新的分析。我们的结果建立在文献中早期工作的基础上，并对其进行了显著的推广。对于某些重尾误差分布和一类一般的设计矩阵，无论调谐参数的选择如何，基于最小二乘法的LASSO都无法实现在正态性假设下导出的近似预言率。相反，我们确定QR-LASSO在比文献中更弱的条件下，对一大类模型实现了接近预言的估计错误率。对于QR-NCP，我们建立了一个新的结果，即在可行区域内的所有局部最优都具有期望的估计精度。我们的分析不仅适用于文献中常用的硬稀疏性设置，也适用于允许许多小系数的软稀疏性设置。我们的方法依赖于使用广义Karush–Kuhn–Tucker条件通过子梯度对正则化QR的全局/局部解的统一刻画。本文的理论建立了高维分位数损失函数的次微分的一个关键性质，它对分析其他高维非光滑问题具有独立的意义。

{"title":"ANALYSIS OF GLOBAL AND LOCAL OPTIMA OF REGULARIZED QUANTILE REGRESSION IN HIGH DIMENSIONS: A SUBGRADIENT APPROACH","authors":"Lan Wang, Xuming He","doi":"10.1017/s0266466622000421","DOIUrl":"https://doi.org/10.1017/s0266466622000421","url":null,"abstract":"Regularized quantile regression (QR) is a useful technique for analyzing heterogeneous data under potentially heavy-tailed error contamination in high dimensions. This paper provides a new analysis of the estimation/prediction error bounds of the global solution of \u0000 \u0000 \u0000 $L_1$\u0000 \u0000 -regularized QR (QR-LASSO) and the local solutions of nonconvex regularized QR (QR-NCP) when the number of covariates is greater than the sample size. Our results build upon and significantly generalize the earlier work in the literature. For certain heavy-tailed error distributions and a general class of design matrices, the least-squares-based LASSO cannot achieve the near-oracle rate derived under the normality assumption no matter the choice of the tuning parameter. In contrast, we establish that QR-LASSO achieves the near-oracle estimation error rate for a broad class of models under conditions weaker than those in the literature. For QR-NCP, we establish the novel results that all local optima within a feasible region have desirable estimation accuracy. Our analysis applies to not just the hard sparsity setting commonly used in the literature, but also to the soft sparsity setting which permits many small coefficients. Our approach relies on a unified characterization of the global/local solutions of regularized QR via subgradients using a generalized Karush–Kuhn–Tucker condition. The theory of the paper establishes a key property of the subdifferential of the quantile loss function in high dimensions, which is of independent interest for analyzing other high-dimensional nonsmooth problems.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49390224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

ECT volume 38 issue 5 Cover and Front matter ECT第38卷第5期封面和封面问题

IF 0.8 4区经济学 Q3 ECONOMICS

Econometric Theory

Pub Date : 2022-10-01 DOI: 10.1017/s0266466622000561

引用次数: 0

ECT volume 38 issue 5 Cover and Back matter ECT第38卷第5期封面和封底

IF 0.8 4区经济学 Q3 ECONOMICS

Econometric Theory

Pub Date : 2022-10-01 DOI: 10.1017/s0266466622000573

引用次数: 0

GUEST EDITORS’ INTRODUCTION PART ONE: SPECIAL DUAL ISSUE OF ECONOMETRIC THEORY ON YALE 2018 CONFERENCE IN HONOR OF PETER C. B. PHILLIPS 特邀编辑导言第一部分:2018年耶鲁大学计量经济理论研讨会特刊，纪念彼得·c·b·菲利普斯

IF 0.8 4区经济学 Q3 ECONOMICS

Econometric Theory

Pub Date : 2022-10-01 DOI: 10.1017/S0266466622000330

D. Andrews, Y. Kitamura, G. Kuersteiner

covariance matrix of time series with increasing dimension. Under a reasonable condition on cross-sectional dependence, it shows that the proposed estimator achieves desirable rates of convergence. It also offers inferential procedures for the mean vector of the time series based on the covariance matrix estimator, and obtains asymptotic normality results for suitably normalized versions of LM/Wald-type statistics.

随维数增加的时间序列协方差矩阵。在合理的横截面相关条件下，表明所提估计器达到了理想的收敛速度。给出了基于协方差矩阵估计的时间序列均值向量的推理过程，并得到了LM/ wald型统计量的适当归一化版本的渐近正态性结果。

引用次数: 0

SEQUENTIALLY ESTIMATING THE STRUCTURAL EQUATION BY POWER TRANSFORMATION 用幂变换顺序估计结构方程

IF 0.8 4区经济学 Q3 ECONOMICS

Econometric Theory

Pub Date : 2022-09-19 DOI: 10.1017/s026646662200038x

Jaedo Choi, H. Moon, J. Cho

This study provides an econometric methodology to test a linear structural relationship among economic variables. We propose the so-called distance-difference (DD) test and show that it has omnibus power against arbitrary nonlinear structural relationships. If the DD-test rejects the linear model hypothesis, a sequential testing procedure assisted by the DD-test can consistently estimate the degree of a polynomial function that arbitrarily approximates the nonlinear structural equation. Using extensive Monte Carlo simulations, we confirm the DD-test’s finite sample properties and compare its performance with the sequential testing procedure assisted by the J-test and moment selection criteria. Finally, through investigation, we empirically illustrate the relationship between the value-added and its production factors using firm-level data from the United States. We demonstrate that the production function has exhibited a factor-biased technological change instead of Hicks-neutral technology presumed by the Cobb–Douglas production function.

本研究提供了一种计量经济学方法来检验经济变量之间的线性结构关系。我们提出了所谓的距离差（DD）检验，并表明它对任意非线性结构关系具有综合能力。如果DD检验拒绝线性模型假设，则在DD检验的辅助下，顺序检验程序可以一致地估计任意逼近非线性结构方程的多项式函数的阶数。使用广泛的蒙特卡罗模拟，我们确认了DD测试的有限样本特性，并将其性能与J测试和力矩选择标准辅助的顺序测试程序进行了比较。最后，通过调查，我们使用美国企业层面的数据实证说明了增值与其生产要素之间的关系。我们证明，生产函数表现出了一种因素偏向的技术变化，而不是Cobb–Douglas生产函数所假设的希克斯中性技术。

引用次数: 0

THE ET INTERVIEW: PROFESSOR PETER SCHMIDT ET访谈：彼得·施密特教授

IF 0.8 4区经济学 Q3 ECONOMICS

Econometric Theory

Pub Date : 2022-08-25 DOI: 10.1017/s0266466622000299

R. Sickles

引用次数: 0

TWO-STEP ESTIMATION OF QUANTILE PANEL DATA MODELS WITH INTERACTIVE FIXED EFFECTS 具有交互固定效应的分位数面板数据模型的两步估计

IF 0.8 4区经济学 Q3 ECONOMICS

Econometric Theory

Pub Date : 2022-08-18 DOI: 10.1017/s0266466622000366

L. Chen

This paper considers the estimation of panel data models with interactive fixed effects where the idiosyncratic errors are subject to conditional quantile restrictions. An easy-to-implement two-step estimator is proposed for the coefficients of the observed regressors. In the first step, the principal component analysis is applied to the cross-sectional averages of the regressors to estimate the latent factors. In the second step, the smoothed quantile regression is used to estimate the coefficients of the observed regressors and the factor loadings jointly. The consistency and asymptotic normality of the estimator are established under large $N,T$ asymptotics. It is found that the asymptotic distribution of the estimator suffers from asymptotic biases, and this paper shows how to correct the biases using both analytical and split-panel jackknife bias corrections. Simulation studies confirm that the proposed estimator performs well with moderate sample sizes.

本文考虑了具有交互固定效应的面板数据模型的估计，其中特殊误差受到条件分位数限制。针对观测回归系数，提出了一种易于实现的两步估计器。在第一步中，将主成分分析应用于回归器的横截面平均值，以估计潜在因素。在第二步中，使用平滑分位数回归来联合估计观察到的回归因子和因子负载的系数。在大的$N，T$渐近条件下，建立了估计量的一致性和渐近正态性。研究发现，估计量的渐近分布存在渐近偏差，本文展示了如何使用分析和分裂面板升降刀偏差校正来校正偏差。仿真研究证实，所提出的估计器在中等样本量下表现良好。

引用次数: 5

RECURSIVE DIFFERENCING FOR ESTIMATING SEMIPARAMETRIC MODELS 估计半参数模型的递推差分

IF 0.8 4区经济学 Q3 ECONOMICS

Econometric Theory

Pub Date : 2022-08-18 DOI: 10.1017/s0266466622000329

Chan Shen, R. Klein

Controlling the bias is central to estimating semiparametric models. Many methods have been developed to control bias in estimating conditional expectations while maintaining a desirable variance order. However, these methods typically do not perform well at moderate sample sizes. Moreover, and perhaps related to their performance, nonoptimal windows are selected with undersmoothing needed to ensure the appropriate bias order. In this paper, we propose a recursive differencing estimator for conditional expectations. When this method is combined with a bias control targeting the derivative of the semiparametric expectation, we are able to obtain asymptotic normality under optimal windows. As suggested by the structure of the recursion, in a wide variety of triple index designs, the proposed bias control performs much better at moderate sample sizes than regular or higher-order kernels and local polynomials.

控制偏差是估计半参数模型的核心。已经开发了许多方法来控制估计条件期望时的偏差，同时保持理想的方差顺序。然而，这些方法通常在中等样本量下表现不佳。此外，可能与它们的性能有关的是，选择非最优窗口时需要进行欠平滑，以确保适当的偏置顺序。本文提出了条件期望的递归差分估计。当该方法与针对半参数期望导数的偏差控制相结合时，我们能够在最优窗口下获得渐近正态性。正如递归结构所表明的那样，在多种三重指数设计中，所提出的偏差控制在中等样本量下的表现要比正则或高阶核和局部多项式好得多。

引用次数: 2

INFERENCE ON A DISTRIBUTION FROM NOISY DRAWS 从有噪声的图中推断出一个分布

IF 0.8 4区经济学 Q3 ECONOMICS

Econometric Theory

Pub Date : 2022-08-18 DOI: 10.1017/s0266466622000378

Koen Jochmans, Martin Weidner

We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other fixed-effect models for panel data. We use an asymptotic embedding where the noise shrinks with the sample size to calculate the leading bias in the empirical distribution arising from the presence of noise. The leading bias in the empirical quantile function is equally obtained. These calculations are new in the literature, where only results on smooth functionals such as the mean and variance have been derived. We provide both analytical and jackknife corrections that recenter the limit distribution and yield confidence intervals with correct coverage in large samples. Our approach can be connected to corrections for selection bias and shrinkage estimation and is to be contrasted with deconvolution. Simulation results confirm the much-improved sampling behavior of the corrected estimators. An empirical illustration on heterogeneity in deviations from the law of one price is equally provided.

我们考虑一种情况，其中随机变量的分布是由该变量的噪声测量的经验分布估计的。例如，在教师增值模型和其他面板数据的固定效应模型中，这是常见的做法。我们使用渐近嵌入，其中噪声随着样本量的减小而减小，以计算由噪声的存在引起的经验分布中的领先偏差。经验分位数函数的领先偏倚是相等的。这些计算在文献中是新的，其中只有光滑函数的结果，如平均值和方差已经导出。我们提供分析和刀切修正，重新中心的极限分布和产率置信区间与正确的覆盖在大样本。我们的方法可以连接到选择偏差和收缩估计的修正，并与反褶积对比。仿真结果证实了修正估计器的采样性能得到了很大的改善。本文还提供了偏离单一价格规律的异质性的实证说明。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Econometric Theory

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀