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Shrinkage Estimation For Nearly Singular Designs

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  • Knight, Keith

Abstract

Shrinkage estimation procedures such as ridge regression and the lasso have been proposed for stabilizing estimation in linear models when high collinearity exists in the design. In this paper, we consider asymptotic properties of shrinkage estimators in the case of “nearly singular” designs.I thank Hannes Leeb and Benedikt Pötscher and also the referees for their valuable comments. This research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.

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  • Knight, Keith, 2008. "Shrinkage Estimation For Nearly Singular Designs," Econometric Theory, Cambridge University Press, vol. 24(2), pages 323-337, April.
    • Handle: RePEc:cup:etheor:v:24:y:2008:i:02:p:323-337_08
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    Cited by:

    1. Reuß, Karsten, 2011. "Determinants of personality and skill development in the Socio-emotional environment during childhood," MPRA Paper 82818, University Library of Munich, Germany.
    2. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.
    3. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    4. Damian Kozbur, 2017. "Testing-Based Forward Model Selection," American Economic Review, American Economic Association, vol. 107(5), pages 266-269, May.
    5. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    6. Damian Kozbur, 2013. "Inference in additively separable models with a high-dimensional set of conditioning variables," ECON - Working Papers 284, Department of Economics - University of Zurich, revised Apr 2018.
    7. Caner, Mehmet & Yıldız, Neşe, 2012. "CUE with many weak instruments and nearly singular design," Journal of Econometrics, Elsevier, vol. 170(2), pages 422-441.
    8. Stefano Maria IACUS & Alessandro DE GREGORIO, 2010. "Adaptive LASSO-type estimation for ergodic diffusion processes," Departmental Working Papers 2010-13, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    9. Damian Kozbur, 2017. "Sharp convergence rates for forward regression in high-dimensional sparse linear models," ECON - Working Papers 253, Department of Economics - University of Zurich, revised Apr 2018.
    10. Mehmet Caner, 2021. "A Starting Note: A Historical Perspective in Lasso," International Econometric Review (IER), Econometric Research Association, vol. 13(1), pages 1-3, March.
    11. Embaye, Weldensie T. & Zereyesus, Yacob A., 2017. "Measuring the value of housing services in household surveys: an application of machine learning approach," 2017 Annual Meeting, February 4-7, 2017, Mobile, Alabama 252851, Southern Agricultural Economics Association.

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