{"id":323,"date":"2017-05-09T10:32:27","date_gmt":"2017-05-09T10:32:27","guid":{"rendered":"http:\/\/jsr.isrt.ac.bd\/?post_type=article&p=323"},"modified":"2017-05-09T10:33:09","modified_gmt":"2017-05-09T10:33:09","slug":"note-weighted-bootstrap-approximation-bickel-rosenblatt-statistic","status":"publish","type":"article","link":"http:\/\/jsr.isrt.ac.bd\/article\/note-weighted-bootstrap-approximation-bickel-rosenblatt-statistic\/","title":{"rendered":"A note on the weighted bootstrap approximation of the Bickel-Rosenblatt Statistic"},"content":{"rendered":"
In this article we propose a weighted bootstrap approximation to the distribution
\nof the supremum (over compact sets) of the classical Bickel-Rosenblatt statistic
\n as well as its \u201cStudentized\u201d version ,
\nwhere is the usual kernel density estimator of the true density . Follow-
\ning Horvath et al. (2000), we showed that the proposed weighted bootstrap
\nmethod is consistent (in capturing the true limiting distributions derived by Bickel
\nand Rosenblatt (1973)). Furthermore, simulation results show that the proposed
\nweighted bootstrap has a much better finite-sample performance than the results
\nbased on asymptotic theory. For comparison purposes, we also consider Efron\u2019s
\n(1979) original bootstrap.<\/p>\n
<\/p>\n