2006
DOI: 10.1524/stnd.2006.24.3.327
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Parametric and semiparametric inference for shape: the role of the scale functional

Abstract: Summary:We are considering the problem of efficient inference on the shape matrix of an elliptic distribution with unspecified location and either (a) fully specified radial density, (b) radial density specified up to a scale parameter, or (c) completely unspecified radial density. Bickel in [1] has shown that efficiencies under (b) and (c), while being strictly less than under (a), coincide: the efficiency loss caused by an unspecified radial density thus is entirely due to the non-specification of its scale … Show more

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Cited by 29 publications
(31 citation statements)
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“…In practice, all choices are essentially equivalent (see [16]). Paindaveine [27] however shows that the information matrix for θ, σ S , and V S is block-diagonal iff the normalization S( ) = | | 1/k is considered.…”
Section: Covariance Scale and Shapementioning
confidence: 99%
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“…In practice, all choices are essentially equivalent (see [16]). Paindaveine [27] however shows that the information matrix for θ, σ S , and V S is block-diagonal iff the normalization S( ) = | | 1/k is considered.…”
Section: Covariance Scale and Shapementioning
confidence: 99%
“…It is natural, though, to see that the perturbed shapes V [16], Section 4). The following notation will be used throughout.…”
Section: Uniform Local Asymptotic Normality (Ulan)mentioning
confidence: 99%
“…Several techniques have been developed for calculating the asymptotic distributions of robust covariance matrix estimators such as the radial distribution approach of Tyler [2] and the approach based on influence functions [3]. Moreover, in recent years deep insights have been gained from the viewpoint of local asymptotic normality (LAN) theory [4][5][6].…”
Section: Introductionmentioning
confidence: 99%
“…Several techniques have been developed for calculating the asymptotic distributions of robust covariance matrix estimators such as the radial distribution approach of Tyler [2] and the approach based on influence functions [3]. Moreover, in recent years deep insights have been gained from the viewpoint of local asymptotic normality (LAN) theory [4][5][6].Let X be a d-dimensional random vector possessing an elliptically symmetric distribution, i.e. it can be represented by X = µ+ΛRU, where U is a k-dimensional random vector, uniformly distributed on the unit hypersphere, R is a nonnegative random variable that is stochastically independent of U, µ ∈ R d , and Λ ∈ R d×k [7,8, p. 42].…”
mentioning
confidence: 99%
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