Center-Outward R-Estimation for Semiparametric VARMA Models

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 asy...

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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 117; no. 538; pp. 925 - 938
Main Authors: Hallin, M., La Vecchia, D., Liu, H.
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 03.04.2022
Taylor & Francis Ltd
Subjects:
Asymptotic methods
Asymptotic properties
Comparative analysis
Comparative studies
comparative study
Competitors
Density
Distribution-freeness
Estimation
Estimators
Experiments
Innovations
Local asymptotic normality
mathematical theory
Measure transportation
Multivariate ranks
Parameter estimation
Quasi-likelihood estimation
Regression analysis
Skew innovation density
statistical analysis
Statistical methods
Statistics
ISSN:0162-1459, 1537-274X, 1537-274X
Online Access:Get full text
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Summary: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 materials . Supplementary materials for this article are available online.
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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2020.1832501