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  • Cited by 6
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    This chapter has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Chernozhukov, Victor Chetverikov, Denis Demirer, Mert Duflo, Esther Hansen, Christian Newey, Whitney and Robins, James 2018. Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, Vol. 21, Issue. 1, p. C1.

    Belloni, Alexandre Chernozhukov, Victor and Kato, Kengo 2018. Valid Post-Selection Inference in High-Dimensional Approximately Sparse Quantile Regression Models. Journal of the American Statistical Association, p. 1.

    Light, Nathaniel Maslov, Denys and Rytchkov, Oleg 2017. Aggregation of Information About the Cross Section of Stock Returns: A Latent Variable Approach. The Review of Financial Studies, Vol. 30, Issue. 4, p. 1339.

    ÇINAROĞLU, Songül 2017. SAĞLIK HARCAMASININ TAHMİNİNDE MAKİNE ÖĞRENMESİ REGRESYON YÖNTEMLERİNİN KARŞILAŞTIRILMASI. Uludağ University Journal of The Faculty of Engineering, Vol. 22, Issue. 2, p. 179.

    Belloni, Alexandre Chernozhukov, Victor and Wei, Ying 2016. Post-Selection Inference for Generalized Linear Models With Many Controls. Journal of Business & Economic Statistics, Vol. 34, Issue. 4, p. 606.

    Chernozhukov, Victor Hansen, Christian and Spindler, Martin 2015. Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach. Annual Review of Economics, Vol. 7, Issue. 1, p. 649.

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  • Print publication year: 2013
  • Online publication date: May 2013

7 - Inference for High-Dimensional Sparse Econometric Models

Summary

Introduction

We consider linear, high-dimensional sparse (HDS) regression models in econometrics. The HDS regression model allows for a large number of regressors, p, which is possibly much larger than the sample size, n, but imposes that the model is sparse. That is, we assume that only sn of these regressors are important for capturing the main features of the regression function. This assumption makes it possible to effectively estimate HDS models by searching for approximately the correct set of regressors. In this chapter, we review estimation methods for HDS models that make use of 1-penalization and then provide a set of novel inference results. We also provide empirical examples that illustrate the potential wide applicability of HDS models and methods in econometrics.

The motivation for considering HDS models comes in part from the wide availability of datasets with many regressors. For example, the American Housing Survey records prices as well as a multitude of features of houses sold, and scanner datasets record prices and numerous characteristics of products sold at a store or on the Internet. HDS models also are partly motivated by the use of series methods in econometrics. Series methods use many constructed or series regressors – regressors formed as transformation of elementary regressors – to approximate regression functions. In these applications, it is important to have a parsimonious yet accurate approximation of the regression function. One way to achieve this is to use the data to select as mall of number of informative terms from among a very large set of control variables or approximating functions.

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Advances in Economics and Econometrics
  • Online ISBN: 9781139060035
  • Book DOI: https://doi.org/10.1017/CBO9781139060035
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