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A general procedure to combine estimators

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  • Lavancier, F.
  • Rochet, P.

Abstract

A general method to combine several estimators of the same quantity is investigated. In the spirit of model and forecast averaging, the final estimator is computed as a weighted average of the initial ones, where the weights are constrained to sum to one. In this framework, the optimal weights, minimizing the quadratic loss, are entirely determined by the mean squared error matrix of the vector of initial estimators. The averaging estimator is built using an estimation of this matrix, which can be computed from the same dataset. A non-asymptotic error bound on the averaging estimator is derived, leading to asymptotic optimality under mild conditions on the estimated mean squared error matrix. This method is illustrated on standard statistical problems in parametric and semi-parametric models where the averaging estimator outperforms the initial estimators in most cases.

Suggested Citation

  • Lavancier, F. & Rochet, P., 2016. "A general procedure to combine estimators," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 175-192.
  • Handle: RePEc:eee:csdana:v:94:y:2016:i:c:p:175-192
    DOI: 10.1016/j.csda.2015.08.001
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    References listed on IDEAS

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    1. Capistrán, Carlos & Timmermann, Allan, 2009. "Forecast Combination With Entry and Exit of Experts," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 428-440.
    2. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    3. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 4, pages 135-196, Elsevier.
    4. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    5. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
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    Cited by:

    1. Filip Staněk, 2023. "Optimal out‐of‐sample forecast evaluation under stationarity," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(8), pages 2249-2279, December.
    2. Wei Zhao & Limin Peng & John Hanfelt, 2022. "Semiparametric latent class analysis of recurrent event data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1175-1197, September.
    3. Frédéric Lavancier & Arnaud Poinas & Rasmus Waagepetersen, 2021. "Adaptive estimating function inference for nonstationary determinantal point processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 87-107, March.
    4. Chernova, O. & Lavancier, F. & Rochet, P., 2020. "Averaging of density kernel estimators," Statistics & Probability Letters, Elsevier, vol. 158(C).
    5. Diaa Al Mohamad, 2018. "Towards a better understanding of the dual representation of phi divergences," Statistical Papers, Springer, vol. 59(3), pages 1205-1253, September.
    6. Torres, Santiago, 2023. "The Oracle Local Polynomial Estimator," Documentos CEDE 20937, Universidad de los Andes, Facultad de Economía, CEDE.
    7. Post, Thierry & Karabatı, Selçuk & Arvanitis, Stelios, 2019. "Robust optimization of forecast combinations," International Journal of Forecasting, Elsevier, vol. 35(3), pages 910-926.
    8. Christophe Ange Napoléon Biscio & Frédéric Lavancier, 2017. "Contrast Estimation for Parametric Stationary Determinantal Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 204-229, March.
    9. Petropoulos, Fotios & Spiliotis, Evangelos & Panagiotelis, Anastasios, 2023. "Model combinations through revised base rates," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1477-1492.
    10. Frédéric Lavancier & Jesper Møller, 2016. "Modelling Aggregation on the Large Scale and Regularity on the Small Scale in Spatial Point Pattern Datasets," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 587-609, June.

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