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An Alternative Asymptotic Analysis of Residual-Based Statistics

Author

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  • Elena Andreou
  • Bas J.M. Werker

Abstract

This paper presents an alternative method to derive the limiting distribution of residual-based statistics. Our method does not impose an explicit assumption of (asymptotic) smoothness of the statistic of interest with respect to the model's parameters. and, thus, is especially useful in cases where such smoothness is difficult to establish. Instead, we use a locally uniform convergence in distribution condition, which is automatically satisfied by residual-based specification test statistics. To illustrate, we derive the limiting distribution of a new functional form specification test for discrete choice models, as well as a runs-based tests for conditional symmetry in dynamic volatility models.

Suggested Citation

  • Elena Andreou & Bas J.M. Werker, 2010. "An Alternative Asymptotic Analysis of Residual-Based Statistics," University of Cyprus Working Papers in Economics 08-2010, University of Cyprus Department of Economics.
    • Handle: RePEc:ucy:cypeua:08-2010
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    File URL: https://papers.econ.ucy.ac.cy/RePEc/papers/8-10.pdf
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    Cited by:

    1. Shu Yang & Yunshu Zhang, 2023. "Multiply robust matching estimators of average and quantile treatment effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 235-265, March.
    2. Andreou, Elena & Werker, Bas J.M., 2015. "Residual-based rank specification tests for AR–GARCH type models," Journal of Econometrics, Elsevier, vol. 185(2), pages 305-331.
    3. Yihui He & Fang Han, 2023. "On propensity score matching with a diverging number of matches," Papers 2310.14142, arXiv.org, revised Nov 2023.
    4. Elena Andreou & Bas J.M. Werker, 2014. "Residual-based Rank Specification Tests for AR-GARCH type models," University of Cyprus Working Papers in Economics 02-2014, University of Cyprus Department of Economics.
    5. Werker, Bas J M & Andreou, Elena, 2013. "Residual-based Rank Specification Tests for AR-GARCH type models," CEPR Discussion Papers 9583, C.E.P.R. Discussion Papers.
    6. 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.
    7. Shu Yang & Jae Kwang Kim, 2020. "Asymptotic theory and inference of predictive mean matching imputation using a superpopulation model framework," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 839-861, September.
    8. Christis Katsouris, 2022. "Partial Sum Processes of Residual-Based and Wald-type Break-Point Statistics in Time Series Regression Models," Papers 2202.00141, arXiv.org, revised Feb 2022.

    More about this item

    Keywords

    Le Cam's third lemma; Local Asymptotic Normality (LAN);

    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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