Complexity penalized support estimation

JOURNAL OF MULTIVARIATE ANALYSIS

卷:88

Article

Klemelä, J

关键词: adaptive estimation;    data-dependent partitions;    quality control;    multivariate data;    tree structured estimators;   

DOI  :  10.1016/S0047-259X(03)00099-X

来源: Elsevier

【 摘 要 】

We consider the estimation of the support of a probability density function with iid observations. The estimator to be considered is a minimizer of a complexity penalized excess mass criterion. We present a fast algorithm for the construction of the estimator. The estimator is able to estimate supports which consists of disconnected regions. We will prove that the estimator achieves minimax rates of convergence up to a logarithmic factor simultaneously over a scale of Holder smoothness classes for the boundary of the support. The proof assumes a sharp boundary for the support. (C) 2003 Elsevier Inc. All rights reserved.

【 授权许可】

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