M-Methods in multivariate linear models
Julio M. Singer,Pranab Kumar Sen +1 more
TLDR
For the multivariate linear model, coordinatewise M-estimators as well as an extension of the Maronna-type M estimators are considered in this article, based on the Jureckova (asymptotic) linearity of M-statistics.About:
This article is published in Journal of Multivariate Analysis.The article was published on 1985-10-01 and is currently open access. It has received 41 citations till now. The article focuses on the topics: Asymptotic distribution & Asymptotic theory (statistics).read more
Citations
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Robust Multivariate Regression
TL;DR: It is shown that the multivariate regression estimator has the appropriate equivariance properties, has a bounded influence function, and inherits the breakdown value of the MCD estimator, which confirms the good finite-sample results obtained from the simulations.
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On preliminary test and shrinkage m-estimation in linear models
TL;DR: In this article, both the preliminary test and shrinkage versions of the usual $M$-estimators are considered and the relative asymptotic risk-efficiency results are studied in detail.
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Robust regression for clustered data with application to binary responses.
TL;DR: A generalization of the GEE procedure, which yields parameter estimates and fitted values that are resistant to influential data, is introduced and RESistant generalized estimating equations (REGEE) include weights in the estimating equations to downweight influential observations or clusters.
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On shrinkage m-estimators of location parameters
TL;DR: For a general class of continuous (and marginally symmetric ) inultivariate distributions, based on suitable M-statistics ( involving bounded but possibly discontinuous score generating functions), shrinkage estimators of location are considered in this article.
References
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Book
Theory of rank tests
TL;DR: In this article, the authors present an elementary theory of rank tests and a set of properties of rank estimators, including asymptotic optimality and efficiency, as well as non-null distributions.
Journal ArticleDOI
Robust $M$-Estimators of Multivariate Location and Scatter
TL;DR: In this article, the robust estimation of the location vector and scatter matrix by means of "$M$-estimators," defined as solutions of the system: √ √ u_1(d_i)(\math{x}_i - \mathbf{t}) = \mathBF{0}$ and $n^{-1]-sum_i u_2(d-i^2)
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Asymptotically most powerful rank-order tests'
TL;DR: In this paper, it was shown that the asymptotic efficiency of rank-order tests is at least twice as large as the efficiency of corresponding parametric tests of Neyman's type.
Journal ArticleDOI
Matrix Derivatives with an Application to an Adaptive Linear Decision Problem
TL;DR: In this article, a theory of matrix differentiation is presented which uses the concept of a matrix of derivative operators, which allows matrix techniques to be used in both the derivation and the description of results.
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Robust Statistical Procedures: Asymptotics and Interrelations
Jana Jurečková,Pranab Kumar Sen +1 more