ASYMPTOTICS FOR GENERAL MULTIVARIATE KERNEL DENSITY DERIVATIVE ESTIMATORS

被引:75
作者
Chacon, Jose E. [1 ]
Duong, Tarn [2 ,3 ]
Wand, M. P. [4 ,5 ]
机构
[1] Univ Extremadura, Dept Matemat, E-06006 Badajoz, Spain
[2] Inst Pasteur, Grp Imagerie & Modelisat, F-75015 Paris, France
[3] CNRS, URA 2582, F-75015 Paris, France
[4] Inst Curie, Mol Mech Intracellular Transport Lab, F-75248 Paris, France
[5] CNRS, UMR 144, F-75248 Paris, France
基金
澳大利亚研究理事会;
关键词
Asymptotic mean integrated squared error; normal scale rule; optimal; unconstrained bandwidth matrices; CONTENT FLOW-CYTOMETRY; BANDWIDTH SELECTION; MATRICES; CHOICE;
D O I
10.5705/ss.2011.036a
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We investigate kernel estimators of multivariate density derivative functions using general (or unconstrained) bandwidth matrix selectors. These density derivative estimators have been relatively less well researched than their density estimator analogues. A major obstacle for progress has been the intractability of the matrix analysis when treating higher order multivariate derivatives. With an alternative vectorization of these higher order derivatives, mathematical intractabilities are surmounted in an elegant and unified framework. The finite sample and asymptotic analysis of squared errors for density estimators are generalized to density derivative estimators. Moreover, we are able to exhibit a closed form expression for a normal scale bandwidth matrix for density derivative estimators. These normal scale bandwidths are employed in a numerical study to demonstrate the gain in performance of unconstrained selectors over their constrained counterparts.
引用
收藏
页码:807 / 840
页数:34
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