TY - JOUR
T1 - On optimal kernel choice for deconvolution
AU - Delaigle, Aurore
AU - Hall, Peter
PY - 2006/9/1
Y1 - 2006/9/1
N2 - In this note we show that, from a conventional viewpoint, there are particularly close parallels between optimal-kernel-choice problems in non-parametric deconvolution, and their better-understood counterparts in density estimation and regression. However, other aspects of these problems are distinctly different, and this property leads us to conclude that "optimal" kernels do not give satisfactory performance when applied to deconvolution. This unexpected result stems from the fact that standard side conditions, which are used to ensure that the familiar kernel-choice problem has a unique solution, do not have statistically beneficial implications for deconvolution estimators. In consequence, certain "sub-optimal" kernels produce estimators that enjoy both greater efficiency and greater visual smoothness.
AB - In this note we show that, from a conventional viewpoint, there are particularly close parallels between optimal-kernel-choice problems in non-parametric deconvolution, and their better-understood counterparts in density estimation and regression. However, other aspects of these problems are distinctly different, and this property leads us to conclude that "optimal" kernels do not give satisfactory performance when applied to deconvolution. This unexpected result stems from the fact that standard side conditions, which are used to ensure that the familiar kernel-choice problem has a unique solution, do not have statistically beneficial implications for deconvolution estimators. In consequence, certain "sub-optimal" kernels produce estimators that enjoy both greater efficiency and greater visual smoothness.
KW - Bandwidth
KW - Ill-posed problem
KW - Inverse problem
KW - Kernel density estimation
KW - Mean integrated squared error
KW - Non-parametric curve estimation
KW - Statistical smoothing
UR - http://www.scopus.com/inward/record.url?scp=33745837056&partnerID=8YFLogxK
U2 - 10.1016/j.spl.2006.04.016
DO - 10.1016/j.spl.2006.04.016
M3 - Article
SN - 0167-7152
VL - 76
SP - 1594
EP - 1602
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
IS - 15
ER -