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Second-order approximation for adaptive regression estimators

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  • Linton, Oliver
  • Xiao, Zhijie

Abstract

We derive asymptotic expansions for semiparametric adaptive regression estimators. In particular, we derive the asymptotic distribution of the second-order effect of an adaptive estimator in a linear regression whose error density is of unknown functional form. We then show how the choice of smoothing parameters influences the estimator through higher order terms. A method of bandwidth selection is defined by minimizing the second-order mean squared error. We examine both independent and time series regressors; we also extend our results to a t-statistic. Monte Carlo simulations confirm the second order theory and the usefulness of the bandwidth selection method.

Suggested Citation

  • Linton, Oliver & Xiao, Zhijie, 2001. "Second-order approximation for adaptive regression estimators," LSE Research Online Documents on Economics 317, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:317
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    Cited by:

    1. Hidehiko Ichimura & Oliver Linton, 2001. "Asymptotic expansions for some semiparametric program evaluation estimators," CeMMAP working papers 04/01, Institute for Fiscal Studies.
    2. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2012. "Optimal inference for instrumental variables regression with non-Gaussian errors," Journal of Econometrics, Elsevier, vol. 167(1), pages 1-15.
    3. 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.
    4. Hafner, C. M., 2022. "Dynamic Autoregressive Liquidity (DArLiQ)," Janeway Institute Working Papers 2206, Faculty of Economics, University of Cambridge.
    5. Tamaki, Kenichiro, 2007. "Second order optimality for estimators in time series regression models," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 638-659, March.

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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