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An Alternative Asymptotic Analysis of Residual-Based Statistics

Author

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  • Andreou, E.

    (Tilburg University, Center For Economic Research)

  • Werker, B.J.M.

    (Tilburg University, Center For Economic Research)

Abstract

This paper offers an alternative technique to derive the limiting distribution of residual-based statistics or, more general, the limiting distribution of statistics with estimated nuisance parameters.This technique allows us to unify many known results on two-stage estimators and tests and we also derive new results.The technique is especially useful in situations where smoothness of the statistic of interest with respect to the parameters to be estimated does not hold or is difficult to establish, e.g., rank-based statistics.We essentially replace this differentiability condition with a distributional invariance property that is often satisfied in specification tests.Our results on statistics that have not been considered before all use nonparametric statistics.On the technical side, we provide a novel approach to the pre-estimation problem using Le Cam s third lemma.The resulting formula for the correction in the limiting variance as a result of pre-estimation some parameters is a simple expression involving some appropriate covariances.The regularity conditions required fairly minimal.Numerous examples show the strength and wide applicability of our approach.

Suggested Citation

  • Andreou, E. & Werker, B.J.M., 2004. "An Alternative Asymptotic Analysis of Residual-Based Statistics," Discussion Paper 2004-56, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:93fe16c1-9f21-4dab-9b73-4dc521ad87d8
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Catani, P.S. & Ahlgren, N.J.C., 2017. "Combined Lagrange multiplier test for ARCH in vector autoregressive models," Econometrics and Statistics, Elsevier, vol. 1(C), pages 62-84.
    2. de Goeij, Peter & Marquering, Wessel, 2005. "The generalized asymmetric dynamic covariance model," Finance Research Letters, Elsevier, vol. 2(2), pages 67-74, June.
    3. Alberto Abadie & Guido W. Imbens, 2016. "Matching on the Estimated Propensity Score," Econometrica, Econometric Society, vol. 84, pages 781-807, March.

    More about this item

    Keywords

    statistics; estimation; testing;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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