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Nearly weighted risk minimal unbiased estimation

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  • Müller, Ulrich K.
  • Wang, Yulong

Abstract

Consider a small-sample parametric estimation problem, such as the estimation of the coefficient in a Gaussian AR(1). We develop a numerical algorithm that determines an estimator that is nearly (mean or median) unbiased, and among all such estimators, comes close to minimizing a weighted average risk criterion. We also apply our generic approach to the median unbiased estimation of the degree of time variation in a Gaussian local-level model, and to a quantile unbiased point forecast for a Gaussian AR(1) process.

Suggested Citation

  • Müller, Ulrich K. & Wang, Yulong, 2019. "Nearly weighted risk minimal unbiased estimation," Journal of Econometrics, Elsevier, vol. 209(1), pages 18-34.
    • Handle: RePEc:eee:econom:v:209:y:2019:i:1:p:18-34
    DOI: 10.1016/j.jeconom.2018.11.016
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    References listed on IDEAS

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    1. Isaiah Andrews & Timothy B. Armstrong, 2017. "Unbiased instrumental variables estimation under known first‐stage sign," Quantitative Economics, Econometric Society, vol. 8(2), pages 479-503, July.
    2. Graham Elliott & Ulrich K. Müller & Mark W. Watson, 2015. "Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis," Econometrica, Econometric Society, vol. 83, pages 771-811, March.
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    Cited by:

    1. Isaiah Andrews & Timothy B. Armstrong, 2017. "Unbiased instrumental variables estimation under known first‐stage sign," Quantitative Economics, Econometric Society, vol. 8(2), pages 479-503, July.
    2. Ulrich K. Müller & Mark W. Watson, 2021. "Spatial Correlation Robust Inference," Working Papers 2021-61, Princeton University. Economics Department..
    3. Timothy B. Armstrong & Patrick Kline & Liyang Sun, 2023. "Adapting to Misspecification," Papers 2305.14265, arXiv.org, revised Jul 2023.
    4. Tetsuya Kaji, 2019. "Theory of Weak Identification in Semiparametric Models," Papers 1908.10478, arXiv.org, revised Aug 2020.
    5. Chenchuan (Mark) Li & Ulrich K. Müller, 2021. "Linear regression with many controls of limited explanatory power," Quantitative Economics, Econometric Society, vol. 12(2), pages 405-442, May.
    6. Wang, Yulong & Xiao, Zhijie, 2022. "Estimation and inference about tail features with tail censored data," Journal of Econometrics, Elsevier, vol. 230(2), pages 363-387.
    7. Isaiah Andrews & Maximilian Kasy, 2019. "Identification of and Correction for Publication Bias," American Economic Review, American Economic Association, vol. 109(8), pages 2766-2794, August.
    8. Ulrich K. Müller & Mark W. Watson, 2022. "Spatial Correlation Robust Inference," Econometrica, Econometric Society, vol. 90(6), pages 2901-2935, November.
    9. Patrick Kline & Christopher Walters, 2019. "Audits as Evidence: Experiments, Ensembles, and Enforcement," Papers 1907.06622, arXiv.org, revised Jul 2019.
    10. Hirano, Keisuke & Wright, Jonathan H., 2022. "Analyzing cross-validation for forecasting with structural instability," Journal of Econometrics, Elsevier, vol. 226(1), pages 139-154.
    11. Tetsuya Kaji, 2021. "Theory of Weak Identification in Semiparametric Models," Econometrica, Econometric Society, vol. 89(2), pages 733-763, March.

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    More about this item

    Keywords

    Mean bias; Median bias; Autoregression; Quantile unbiased forecast;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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