Annals of Statistics

Semiparametrically efficient inference based on signed ranks in symmetric independent component models

Pauliina Ilmonen and Davy Paindaveine

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We consider semiparametric location-scatter models for which the p-variate observation is obtained as X = ΛZ + μ, where μ is a p-vector, Λ is a full-rank p × p matrix and the (unobserved) random p-vector Z has marginals that are centered and mutually independent but are otherwise unspecified. As in blind source separation and independent component analysis (ICA), the parameter of interest throughout the paper is Λ. On the basis of n i.i.d. copies of X, we develop, under a symmetry assumption on Z, signed-rank one-sample testing and estimation procedures for Λ. We exploit the uniform local and asymptotic normality (ULAN) of the model to define signed-rank procedures that are semiparametrically efficient under correctly specified densities. Yet, as is usual in rank-based inference, the proposed procedures remain valid (correct asymptotic size under the null, for hypothesis testing, and root-n consistency, for point estimation) under a very broad range of densities. We derive the asymptotic properties of the proposed procedures and investigate their finite-sample behavior through simulations.

Article information

Ann. Statist., Volume 39, Number 5 (2011), 2448-2476.

First available in Project Euclid: 30 November 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G10: Hypothesis testing
Secondary: 62G20: Asymptotic properties 62H99: None of the above, but in this section

Independent component analysis local asymptotic normality rank-based inference semiparametric efficiency signed ranks


Ilmonen, Pauliina; Paindaveine, Davy. Semiparametrically efficient inference based on signed ranks in symmetric independent component models. Ann. Statist. 39 (2011), no. 5, 2448--2476. doi:10.1214/11-AOS906.

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Supplemental materials

  • Supplementary material: Further results on tests and a proof of Theorem 4.3. This supplement provides a simple explicit expression for the proposed test statistics, derives local asymptotic powers of the corresponding tests, and presents simulation results for hypothesis testing. It also gives a proof of Theorem 4.3.