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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," Econometric Theory, Cambridge University Press, vol. 17(5), pages 984-1024, October.
    • Handle: RePEc:cup:etheor:v:17:y:2001:i:05:p:984-1024_17
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    Cited by:

    1. 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.
    2. Hidehiko Ichimura & Oliver Linton, 2001. "Asymptotic expansions for some semiparametric program evaluation estimators," CeMMAP working papers 04/01, Institute for Fiscal Studies.
    3. Hafner, Christian & Linton, Oliver & Wang, Linqi, 2022. "Dynamic Autoregressive Liquidity (DArLiQ)," LIDAM Discussion Papers ISBA 2022009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. 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.
    5. 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.

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    JEL classification:

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

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