Affine-equivariant inference for multivariate location under Lp loss functions
Lp 损失下多元位置的仿射等变推断
We consider the fundamental problem of estimating the location of a d-variate probability measure under an Lp loss function. The naive estimator, that minimizes the usual empirical Lp risk, has a known asymptotic behavior but suffers from several deficiencies for p≠2, the most important one being the lack of equivariance under general affine transformations. In this work, we introduce a collection of Lp location estimators μˆnp,ℓ that minimize the size of suitable…