IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v186y2015i2p345-366.html
   My bibliography  Save this article

Some new asymptotic theory for least squares series: Pointwise and uniform results

Author

Listed:
  • Belloni, Alexandre
  • Chernozhukov, Victor
  • Chetverikov, Denis
  • Kato, Kengo

Abstract

In econometric applications it is common that the exact form of a conditional expectation is unknown and having flexible functional forms can lead to improvements over a pre-specified functional form, especially if they nest some successful parametric economically-motivated forms. Series method offers exactly that by approximating the unknown function based on k basis functions, where k is allowed to grow with the sample size n to balance the trade off between variance and bias. In this work we consider series estimators for the conditional mean in light of four new ingredients: (i) sharp LLNs for matrices derived from the non-commutative Khinchin inequalities, (ii) bounds on the Lebesgue factor that controls the ratio between the L∞ and L2-norms of approximation errors, (iii) maximal inequalities for processes whose entropy integrals diverge at some rate, and (iv) strong approximations to series-type processes.

Suggested Citation

  • Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2015. "Some new asymptotic theory for least squares series: Pointwise and uniform results," Journal of Econometrics, Elsevier, vol. 186(2), pages 345-366.
  • Handle: RePEc:eee:econom:v:186:y:2015:i:2:p:345-366 DOI: 10.1016/j.jeconom.2015.02.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030440761500038X
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    2. Xiaohong Chen & Timothy M. Christensen, 2013. "Optimal uniform convergence rates for sieve nonparametric instrumental variables regression," CeMMAP working papers CWP56/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-345, March.
    4. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
    5. Huang, Jianhua Z., 2003. "Asymptotics for polynomial spline regression under weak conditions," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 207-216, November.
    6. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Iv'an Fern'andez-Val, 2011. "Conditional Quantile Processes based on Series or Many Regressors," Papers 1105.6154, arXiv.org, revised Jul 2017.
    7. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76 Elsevier.
    8. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximation of suprema of empirical processes," CeMMAP working papers CWP44/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Xiaohong Chen & Timothy Christensen, 2013. "Optimal Uniform Convergence Rates for Sieve Nonparametric Instrumental Variables Regression," Cowles Foundation Discussion Papers 1923, Cowles Foundation for Research in Economics, Yale University.
    10. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, March.
    11. Cattaneo, Matias D. & Farrell, Max H., 2013. "Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators," Journal of Econometrics, Elsevier, vol. 174(2), pages 127-143.
    12. Eastwood, Brian J. & Gallant, A. Ronald, 1991. "Adaptive Rules for Seminonparametric Estimators That Achieve Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 7(03), pages 307-340, September.
    13. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2012. "Alternative Asymptotics and the Partially Linear Model with Many Regressors," CREATES Research Papers 2012-02, Department of Economics and Business Economics, Aarhus University.
    2. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2015. "Inference in Linear Regression Models with Many Covariates and Heteroskedasticity," Papers 1507.02493, arXiv.org, revised Jan 2017.
    3. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Iv'an Fern'andez-Val, 2011. "Conditional Quantile Processes based on Series or Many Regressors," Papers 1105.6154, arXiv.org, revised Jul 2017.
    4. Michael Jansson & Demian Pouzo, 2017. "Some Large Sample Results for the Method of Regularized Estimators," Papers 1712.07248, arXiv.org.
    5. Denis Chetverikov & . ., 2016. "On cross-validated Lasso," CeMMAP working papers CWP47/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Breunig, Christoph, 2017. "Testing Missing At Random Using Instrumental Variables," Rationality and Competition Discussion Paper Series 59, CRC TRR 190 Rationality and Competition.
    7. Chaohua Dong & Jiti Gao & Oliver Linton, 2017. "High dimensional semiparametric moment restriction models," Monash Econometrics and Business Statistics Working Papers 17/17, Monash University, Department of Econometrics and Business Statistics.
    8. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2015. "Constrained conditional moment restriction models," CeMMAP working papers CWP59/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Christoph Breunig & Stefan Hoderlein, 2016. "Nonparametric Specification Testing in Random Parameter Models," Boston College Working Papers in Economics 897, Boston College Department of Economics.
    10. Hidehiko Ichimura & Whitney K. Newey, 2015. "The Influence Function of Semiparametric Estimators," CIRJE F-Series CIRJE-F-985, CIRJE, Faculty of Economics, University of Tokyo.
    11. Joachim Freyberger & Andreas Neuhierl & Michael Weber, 2017. "Dissecting Characteristics Nonparametrically," CESifo Working Paper Series 6391, CESifo Group Munich.
    12. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    13. Sun, Yiguo & Malikov, Emir, 2017. "Estimation and Inference in Functional-Coefficient Spatial Autoregressive Panel Data Models with Fixed Effects," MPRA Paper 83671, University Library of Munich, Germany.
    14. Holland, Ashley D., 2017. "Penalized spline estimation in the partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 211-235.
    15. Zhao, Weihua & Lian, Heng, 2016. "Local asymptotics for nonparametric quantile regression with regression splines," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 209-215.
    16. Samuele CENTORRINO & Jeffrey S. RACINE, 2017. "Semiparametric Varying Coefficient Models with Endogenous Covariates," Annals of Economics and Statistics, GENES, issue 128, pages 261-295.
    17. repec:eee:econom:v:200:y:2017:i:1:p:1-16 is not listed on IDEAS
    18. Christoph Breunig & Enno Mammen & Anna Simoni, "undated". "Nonparametric Estimation in case of Endogenous Selection," SFB 649 Discussion Papers SFB649DP2015-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    19. Babii, Andrii, 2017. "Honest confidence sets in nonparametric IV regression and other ill-posed models," TSE Working Papers 17-803, Toulouse School of Economics (TSE).
    20. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2017. "Nonparametric Estimation in Case of Endogenous Selection," Rationality and Competition Discussion Paper Series 58, CRC TRR 190 Rationality and Competition.
    21. Hidehiko Ichimura & Whitney K. Newey, 2017. "The influence function of semiparametric estimators," CeMMAP working papers CWP06/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    22. Whitney K. Newey & James M. Robins, 2017. "Cross-fitting and fast remainder rates for semiparametric estimation," CeMMAP working papers CWP41/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    23. Christoph Breunig, 2017. "Testing Missing at Random using Instrumental Variables," SFB 649 Discussion Papers SFB649DP2017-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    24. Christoph Breunig & Stefan Hoderlein, "undated". "Specification Testing in Random Coefficient Models," SFB 649 Discussion Papers SFB649DP2015-053, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    Least squares series; Strong approximations; Uniform confidence bands;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:186:y:2015:i:2:p:345-366. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.