Center-Outward R-Estimation for Semiparametric VARMA Models

Hallin, Marc and La Vecchia, Davide and Liu, Hang (2022) Center-Outward R-Estimation for Semiparametric VARMA Models. Journal of the American Statistical Association, 117 (538). pp. 925-938. ISSN 0162-1459

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We propose a new class of R-estimators for semiparametric VARMA models in which the innovation density plays the role of the nuisance parameter. Our estimators are based on the novel concepts of multivariate center-outward ranks and signs. We show that these concepts, combined with Le Cam's asymptotic theory of statistical experiments, yield a class of semiparametric estimation procedures, which are efficient (at a given reference density), root-$n$ consistent, and asymptotically normal under a broad class of (possibly non elliptical) actual innovation densities. No kernel density estimation is required to implement our procedures. A Monte Carlo comparative study of our R-estimators and other routinely-applied competitors demonstrates the benefits of the novel methodology, in large and small sample. Proofs, computational aspects, and further numerical results are available in the supplementary material.

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Journal Article
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Journal of the American Statistical Association
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15 Jun 2021 08:35
Last Modified:
22 Nov 2022 09:34