R-estimation in semiparametric dynamic location-scale models

Hallin, Marc; Vecchia, Davide La

doi:10.1016/j.jeconom.2016.08.002

Cited by 10 publications

(2 citation statements)

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“…and, consequently, (n) a and m (n) e both are o(n −1/2 ) (see Lemma 1 in Hallin and La Vecchia (2017)) and m, m (n) a , and m (n) e can be omitted in Proposition 3.2. That simplification, however, is no longer valid when d > 1.…”

Section: Hájek Asymptotic Representationmentioning

confidence: 99%

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Rank-Based Testing for Semiparametric VAR Models: a measure transportation approach

Hallin¹,

Vecchia²,

Liu³

2020

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We develop a class of tests for semiparametric vector autoregressive (VAR) models with unspecified innovation densities, based on the recent measure-transportation-based concepts of multivariate center-outward ranks and signs. We show that these concepts, combined with Le Cam's asymptotic theory of statistical experiments, yield novel testing procedures, which (a) are valid under a broad class of innovation densities (possibly non-elliptical, skewed, and/or with infinite moments), (b) are optimal (locally asymptotically maximin or most stringent) at selected ones, and (c) are robust against additive outliers. In order to do so, we establish a Hájek asymptotic representation result, of independent interest, for a general class of center-outward rank-based serial statistics. As an illustration, we consider the problems of testing the absence of serial correlation in multiple-output and possibly non-linear regression (an extension of the classical Durbin-Watson problem) and the sequential identification of the order p of a vector autoregressive (VAR(p)) model. A Monte Carlo comparative study of our tests and their routinely-applied Gaussian competitors demonstrates the benefits (in terms of size, power, and robustness) of our methodology; these benefits are particularly significant in the presence of asymmetric and leptokurtic innovation densities. A real data application concludes the paper.

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Section: Hájek Asymptotic Representationmentioning

confidence: 99%

“…Here are three examples of sensible choices extending scores that are widely applied in the univariate (see e.g. Hallin and La Vecchia (2017)) and the elliptical multivariate setting (see Hallin and Paindaveine (2004a)). Note that for these scores, the centering term m (n) a for Γ…”

Section: Some Standard Score Functionsmentioning

confidence: 99%