Jones, M. C.
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Recently, much progress has been made on understanding the bandwidth selection problem in kernel density estimation. Here, analogous questions are considered for extensions to the basic problem, namely, for estimating derivatives, using ‘better’ kernel estimators, and for the multivariate case. In basic kernel density estimation, recent advances have resulted in considerable improvements being made over ‘moderate’ methods such as least squares cross-validation. Here, it is argued that, in the first two extension cases, the performance of moderate methods deteriorates even more, so that the necessity for ‘improved’ methods — and indeed their potential in theory if not necessarily in practice — is greatly increased. Rather extraordinary things happen, however, when higher dimensions are considered.
|Item Type:||Book Chapter|
|Copyright Holders:||1991 Kluwer Academic Publishers|
|Extra Information:||Proceedings of the NATO Advanced Study Institute, Spetses, Greece, July 29-August 10, 1990|
|Keywords:||adaptive selection; convergence rates; cross-validation; estimating derivatives; functional estimation; higher order kernels; multivariate estimation; smoothing|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics|
|Depositing User:||Sarah Frain|
|Date Deposited:||09 Mar 2011 15:57|
|Last Modified:||09 Mar 2011 16:11|
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