On Locally Adaptive Density Estimation
作者:
StephanR. Sain,
DavidW. Scott,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1996)
卷期:
Volume 91,
issue 436
页码: 1525-1534
ISSN:0162-1459
年代: 1996
DOI:10.1080/01621459.1996.10476720
出版商: Taylor & Francis Group
关键词: Binning;Cross-validation;Kernel function;Variable bandwidth
数据来源: Taylor
摘要:
Theoretical and practical aspects of the sample-point adaptive positive kernel density estimator are examined. A closed-form expression for the mean integrated squared error is obtained through the device of preprocessing the data by binning. With this expression, the exact behavior of the optimally adaptive smoothing parameter function is studied for the first time. The approach differs from most earlier techniques in that bias of the adaptive estimator remainsO(h2) and is not “improved” to the rateO(h4). A practical algorithm is constructed using a modification of least squares cross-validation. Simulated and real examples are presented, including comparisons with a fixed bandwidth estimator and a fully automatic version of Abramson's adaptive estimator. The results are very promising.
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