Estimation under l1-symmetry

[摘要] The estimation of the location parameter of an l(1)-symmetric distribution is considered. Specifically when a p-dimensional random vector has a distribution that is a mixture of uniform distributions on the l(1)-sphere, we investigate a general class of estimators of the form delta = X + g. Under the usual quadratic loss, domination of 6 over X is obtained through the partial differential inequality 4 div g + 2X (.) partial derivative(2)g + parallel togparallel to(2) less than or equal to 0 and a new superharmonicity-type-like notion adapted to the l(1)-context. Specifically the condition of l(1)-superharmonicity is that 2Deltaf + X (.) del(3) f less than or equal to 0 and div del(3) f greater than or equal to 0 as compared to the usual (e,) condition Deltaf less than or equal to 0. (C) 2002 Elsevier Science.

[发布日期] 2002-11-01

[关键词] l(1)-norm;l(1)-symmetry;estimation;quadratic loss;minimaxity;partial differential inequalities;l(1)-superharmonicity