Boundary kernels for adaptive density estimators on regions with irregular boundaries

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Marshall, Jonathan C.¹  Hazelton, Martin L.¹ 

[1] Massey Univ, Inst Fundamental Sci Stat, Palmerston North, New Zealand

关键词: Adaptive smoothing;    Boundary bias;    Edge effects;    Kernel estimator;    Variable bandwidth;   

DOI  :  10.1016/j.jmva.2009.09.003

来源: Elsevier

【 摘 要 】

In some applications of kernel density estimation the data may have a highly non-uniform distribution and be confined to a compact region. Standard fixed bandwidth density estimates can struggle to cope with the spatially variable smoothing requirements, and will be subject to excessive bias at the boundary of the region. While adaptive kernel estimators can address the first of these issues, the study of boundary kernel methods has been restricted to the fixed bandwidth context. We propose a new linear boundary kernel which reduces the asymptotic order of the bias of an adaptive density estimator at the boundary, and is simple to implement even on an irregular boundary. The properties of this adaptive boundary kernel are examined theoretically. In particular, we demonstrate that the asymptotic performance of the density estimator is maintained when the adaptive bandwidth is defined in terms of a pilot estimate rather than the true underlying density. We examine the performance for finite sample sizes numerically through analysis of simulated and real data sets. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free