Estimation of regression functions via penalization andthe framework two examplesselection 3. Highdimensional models are characterized by having a number of unknown parameters that is not vanishingly small relative to the sample size. Editorialjournalofeconometrics1862015277279 279 bootstrapobservationsaregeneratedrecursivelyusingtheestimatedstructureofthemodel,resamplingfromtheresidualsis. Clt for largest eigenvalues and unit root tests for high. In this article, we study the problem of testing the mean vectors of high dimensional data in both one. Particular attention will be given to precise estimation. Econometric estimation with highdimensional moment equalities zhentao shi the chinese university of hong kong september 23, 2015 zhentao shi cuhk highdimensional moments hku 1 44. High dimensional sparse models arise in situations.
Hansen 2000, 20201 university of wisconsin department of economics this revision. Econometric estimation with highdimensional moment. Estimation of regression functions via penalization and selection3. A number of papers have begun to investigate estimation of hdsms, focusing primarily on penalized mean regression, with the 1norm acting as a penalty function 7, 12, 22, 26, 32, 34. Title as it appears in mit commencement exercises program, june 5, 2015. Thus, the random projection method can link the testing problem in both high and low dimensions, and in the low dimensional setting, by setting k n, it includes the grs test as. Inference for highdimensional sparse econometric models. One of the tools to analyze large, highdimensional data is the panel data model. High dimensional econometrics mehmet caner and anders bredahl kock february 24, 2017 recent years have seen a massive increase in the availability of large data sets.
High dimensional econometrics and regularized gmm by alexandre belloni, victor chernozhukov, denis chetverikov, christian hansen, and kengo kato abstract. Testing highdimensional linear asset pricing models. Oracle efficient estimation and forecasting with the adaptive lasso and the adaptive group lasso in vector autoregressions. Estimation ofregression functions via penalization and selection 3. Modelling dependence in high dimensions with factor copulas dong hwan oh and andrew j. This chapter presents key concepts and theoretical results for analyzing estimation and inference in high dimensional models. Testing heteroscedasticity of the errors is a major challenge in high dimensional regressions where the number of covariates is large compared to the sample size. High dimensional models are characterized by having a number of unknown parameters that is not vanishingly small relative to the sample size. Here, too, the crucial ingredient is the use of orthogonal. Focusing on linear and nonparametric regression frame. Journal of the royal statistical society series b 76, 627649.
Clt for largest eigenvalues and unit root tests for high dimensional nonstationary time series bo zhang and guangming panyand jiti gaoz july 26, 2016 abstract this paper rst considers some testing issues for a vector of high dimensional time series. Highdimensional methods and inference on structural and. In this chapter we discuss conceptually high dimensional sparse econometric models as well as estimation of these models using l1penalization and postl1penalization methods. High dimensional models have always been of interest in econometrics and have recently been gaining in popularity. Highdimensional econometrics and generalized gmm request pdf.
Modelling dependence in high dimensions with factor copulas. Highdimensional econometrics and generalized gmm deepai. In their setting, a large number of ivs all meet the orthogonality condition zero correlation with the structural. Essays in highdimensional econometrics and model selection. High dimensional covariance matrix estimation using a factor model. An introduction alexandre belloni and victor chernozhukov abstract in this chapter we discuss conceptually high dimensional sparse econometric models as well as estimation of these models using 1penalization and post1penalization methods. Highdimensional sparse econometric models, an introduction alexandre belloni ice, july 2011 alexandre belloni highdimensional sparse econometrics.
Estimation and inference on te in a general model conclusion econometrics of big data. Robust high dimensional volatility matrix estimation for high frequency factor model. High dimensional econometrics and regularized gmm, papers 1806. High dimensional sparse models arise in situations where many regressors or series terms are available and the regression function is wellapproximated by a parsimonious, yet unknown set of regressors. This article is about estimation and inference methods for high dimensional sparse hds regression models in econometrics. In this example, abstract away from the estimation questions, using populationcensus data. These two papers do not consider the estimation with high dimensional moments. Estimation of regression functions via penalization and selection 3. February, 2020 comments welcome 1this manuscript may be printed and reproduced for individual or instructional use, but may not be printed for. Pdf testing for heteroscedasticity in highdimensional. The recent interest in these models is due to both the availability of rich, modern data sets and to advances in the analysis of high dimensional settings, such as the emergence of high dimensional central limit theorems and. High dimensional econometrics and identification grew out of research work on the identification and high dimensional econometrics that we have collaborated on over the years, and it aims.
We examine covariance matrix estimation in the asymptotic framework. High dimensional econometrics and regularized gmm with a. In this course we will cover some of the techniques that have been developed to analyze such data sets. Robust highdimensional volatility matrix estimation for highfrequency factor model. Estimation and inference on te in a general modelconclusion econometrics of big data. Highdimensional econometrics and identification 178 pages. Request pdf highdimensional econometrics and generalized gmm this chapter presents key concepts and theoretical results for analyzing estimation and inference in highdimensional models. Jun 26, 2011 in this chapter we discuss conceptually high dimensional sparse econometric models as well as estimation of these models using l1penalization and postl1penalization methods. Econometric estimation with high dimensional moment equalities zhentao shi the chinese university of hong kong september 23, 2015 zhentao shi cuhk high dimensional moments hku 1 44. Econometric estimation with highdimensional moment equalities.
We first present results in a framework where estimators of parameters of interest may be represented directly as approximate means. High dimensional thresholded regression and shrinkage effect. Highdimensional sparse econometric models, an introduction. Summer institute 20 econometric methods for high dimensional data july 1516, 20 victor chernozhukov, matthew gentzkow, christian hansen, jesse shapiro, matthew taddy, organizers complete index of summer institute econometric lectures matthew taddy prediction with high dimensional data 1. Bai and ng, 2009, bai and ng, 2010 and belloni et al. High dimensional problems in econometrics sciencedirect. Journal of econometrics, 208, 522 manuscript fan, j. High dimensional covariance matrix estimation using a factor. Uniform inference in high dimensional dynamic panel data models with approximately sparse fixed effects volume 35 issue 2 anders bredahl kock, haihan tang. Estimation and inference with econometrics of high dimensional sparse models p much larger than n victor chernozhukov christian hansen nber, july 20 vc and ch econometrics of high dimensional sparse models.
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