Estimation under l1-Symmetry

Dominique Fourdrinier and Anne-Sophie Lemaire

Journal of Multivariate Analysis, 2002, vol. 83, issue 2, 303-323

Abstract: The estimation of the location parameter of an l1-symmetric distribution is considered. Specifically when a p-dimensional random vector has a distribution that is a mixture of uniform distributions on the l1-sphere, we investigate a general class of estimators of the form [delta]=X+g. Under the usual quadratic loss, domination of [delta] over X is obtained through the partial differential inequality 4 div g+2Xc[not partial differential]2g+ ||g||2[less-than-or-equals, slant]0 and a new superharmonicity-type-like notion adapted to the l1-context. Specifically the condition of l1-superharmonicity is that 2[Delta]f+Xc[backward difference]3f[less-than-or-equals, slant]0 and div [backward difference]3f[greater-or-equal, slanted]0 as compared to the usual (l2) condition [Delta]f[less-than-or-equals, slant]0.

Keywords: l1-norm; l1-symmetry; estimation; quadratic; loss; minimaxity; partial; differential; inequalities; l1-superharmonicity (search for similar items in EconPapers)
Date: 2002
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