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Rates of Expansions for Functional Estimators

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A Correction to this article was published on 23 December 2021

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Abstract

In this paper, we summarize results on convergence rates of various kernel based non- and semiparametric estimators, focusing on the impact of insufficient distributional smoothness, possibly unknown smoothness and even non-existence of density. In the presence of a possible lack of smoothness and the uncertainty about smoothness, methods of safeguarding against this uncertainty are surveyed with emphasis on nonconvex model averaging. This approach can be implemented via a combined estimator that selects weights based on minimizing the asymptotic mean squared error. In order to evaluate the finite sample performance of these and similar estimators we argue that it is important to account for possible lack of smoothness.

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Change history

  • 23 December 2021

    The original online published version of the article as been updated due to Open access cancellation.

  • 23 December 2021

    A Correction to this paper has been published: https://doi.org/10.1007/s40953-021-00280-w

Notes

  1. As a referee pointed out, the estimation of the degree of smoothness bears similarity to the test for smoothness in Mukherjee et al. (2016) in the context of adaptive Lepski estimation of nonlinear functionals of density.

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Acknowledgements

We thank an anonymous referee for valuable comments. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC)

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Natural Sciences and Engineering Research Council of Canada (NSERC).

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Authors and Affiliations

  1. Department of Economics, Dalhousie University, Halifax, Canada

    Yulia Kotlyarova

  2. Department of Economics, London School of Economics, London, UK

    Marcia M. A. Schafgans

  3. Department of Economics, McGill University and CIREQ, Montreal, Canada

    Victoria Zinde-Walsh

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  1. Yulia Kotlyarova
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Correspondence to Victoria Zinde-Walsh.

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Kotlyarova, Y., Schafgans, M.M.A. & Zinde-Walsh, V. Rates of Expansions for Functional Estimators. J. Quant. Econ. 19 (Suppl 1), 121–139 (2021). https://doi.org/10.1007/s40953-021-00266-8

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