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The Efficiency Gap

Timo Dimitriadis, Tobias Fissler, Johanna Ziegel

arXiv 27 Oct 2020 · Mathematics — Statistics Theory · 2 citations (OpenAlex)

arXiv:2010.14146 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Parameter estimation via M- and Z-estimation is equally powerful in semiparametric models for one-dimensional functionals due to a one-to-one relation between corresponding loss and identification functions via integration and differentiation. For multivariate functionals such as multiple moments, quantiles, or the pair (Value at Risk, Expected Shortfall), this one-to-one relation fails and not every identification function possesses an antiderivative. The most important implication is an efficiency gap: The most efficient Z-estimator often outperforms the most efficient M-estimator. We theoretically establish this phenomenon for multiple quantiles at different levels and for the pair (Value at Risk, Expected Shortfall), and illustrate the gap numerically. Our results further give guidance for pseudo-efficient M-estimation for semiparametric models of the Value at Risk and Expected Shortfall.

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71
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207
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71
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Dimitriadis, T., Fissler, T., and Ziegel, J (2022) Characterizing M-estimators self1.0002010100%
2Fissler, T. and Ziegel, J. F (2016) Higher order elicitability and Osband's principle self1.000157100%
3Barendse, S (2022) Efficiently Weighted Estimation of Tail and Interquantile Expectations1.000135100%
4Newey, W. K. and McFadden, D (1994) Large sample estimation and hypothesis testing1.000106100%
5Chamberlain, G (1987) Asymptotic efficiency in estimation with conditional moment restrictions1.000104100%
6Newey, W. K (1993) Efficient Estimation of Models with Conditional Moment Restrictions1.00085100%
7Gneiting, T (2011) Making and Evaluating Point Forecasts1.00075100%
8Patton, A. J., Ziegel, J. F., and Chen, R (2019) Dynamic semiparametric models for expected shortfall (and value-at-risk) self1.00073100%
9Komunjer, I. and Vuong, Q (2010) Semiparametric efficiency bound in time-series models for conditional quantiles1.00064100%
10Hansen, L. P (1985) A method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators1.00053100%

Showing the top 10 of 71 scored citations.