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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
Econometric Theory Pub Date : 2022-10-28 DOI: 10.1017/s0266466622000457
P. Maréchal, L. Simar, A. Vanhems
{"title":"A MOLLIFIER APPROACH TO THE DECONVOLUTION OF PROBABILITY DENSITIES","authors":"P. Maréchal, L. Simar, A. Vanhems","doi":"10.1017/s0266466622000457","DOIUrl":"https://doi.org/10.1017/s0266466622000457","url":null,"abstract":"\u0000 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.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41454301","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: 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
Econometric Theory Pub Date : 2022-10-18 DOI: 10.1017/s0266466622000421
Lan Wang, Xuming He
{"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
Econometric Theory Pub Date : 2022-10-01 DOI: 10.1017/s0266466622000561
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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
Econometric Theory Pub Date : 2022-10-01 DOI: 10.1017/s0266466622000573
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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
Econometric Theory Pub Date : 2022-10-01 DOI: 10.1017/S0266466622000330
D. Andrews, Y. Kitamura, G. Kuersteiner
{"title":"GUEST EDITORS’ INTRODUCTION PART ONE: SPECIAL DUAL ISSUE OF ECONOMETRIC THEORY ON YALE 2018 CONFERENCE IN HONOR OF PETER C. B. PHILLIPS","authors":"D. Andrews, Y. Kitamura, G. Kuersteiner","doi":"10.1017/S0266466622000330","DOIUrl":"https://doi.org/10.1017/S0266466622000330","url":null,"abstract":"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.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":"38 1","pages":"841 - 844"},"PeriodicalIF":0.8,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47866495","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: 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
Econometric Theory Pub Date : 2022-09-19 DOI: 10.1017/s026646662200038x
Jaedo Choi, H. Moon, J. Cho
{"title":"SEQUENTIALLY ESTIMATING THE STRUCTURAL EQUATION BY POWER TRANSFORMATION","authors":"Jaedo Choi, H. Moon, J. Cho","doi":"10.1017/s026646662200038x","DOIUrl":"https://doi.org/10.1017/s026646662200038x","url":null,"abstract":"\u0000 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.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46685465","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: 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
Econometric Theory Pub Date : 2022-08-25 DOI: 10.1017/s0266466622000299
R. Sickles
{"title":"THE ET INTERVIEW: PROFESSOR PETER SCHMIDT","authors":"R. Sickles","doi":"10.1017/s0266466622000299","DOIUrl":"https://doi.org/10.1017/s0266466622000299","url":null,"abstract":"","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":"39 1","pages":"881 - 899"},"PeriodicalIF":0.8,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46867149","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: 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
Econometric Theory Pub Date : 2022-08-18 DOI: 10.1017/s0266466622000366
L. Chen
{"title":"TWO-STEP ESTIMATION OF QUANTILE PANEL DATA MODELS WITH INTERACTIVE FIXED EFFECTS","authors":"L. Chen","doi":"10.1017/s0266466622000366","DOIUrl":"https://doi.org/10.1017/s0266466622000366","url":null,"abstract":"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 \u0000\u0000 \u0000 \u0000 \u0000$N,T$\u0000\u0000 \u0000 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.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42095015","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: 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
Econometric Theory Pub Date : 2022-08-18 DOI: 10.1017/s0266466622000329
Chan Shen, R. Klein
{"title":"RECURSIVE DIFFERENCING FOR ESTIMATING SEMIPARAMETRIC MODELS","authors":"Chan Shen, R. Klein","doi":"10.1017/s0266466622000329","DOIUrl":"https://doi.org/10.1017/s0266466622000329","url":null,"abstract":"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.\u0000","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48761800","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: 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
Econometric Theory Pub Date : 2022-08-18 DOI: 10.1017/s0266466622000378
Koen Jochmans, Martin Weidner
{"title":"INFERENCE ON A DISTRIBUTION FROM NOISY DRAWS","authors":"Koen Jochmans, Martin Weidner","doi":"10.1017/s0266466622000378","DOIUrl":"https://doi.org/10.1017/s0266466622000378","url":null,"abstract":"<p>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.</p>","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":"5 2-5","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525633","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: 0
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