ON THE EXACT AND THE APPROXIMATE MEAN INTEGRATED SQUARE ERROR FOR THE KERNEL DISTRIBUTION FUNCTION ESTIMATOR

Abdel-Razzaq Mugdadi, Rawan Bani-Melhem

Abstract


The asymptotic mean integrated square error
(AMISE) is used as an approximate measure of error for the
mean integrated square error (MISE). The exact MISE for kernel
density estimator is discussed by Marron and Wand [1]. In this
investigation we discuss the exact MISE and the AMISE for
the cumulative distribution function estimate. Also, we compare
between the optimal bandwidth that minimize the AMISE and
that minimize the MISE. In addition, through simulations these
optimal bandwidths are compared with the bandwidth selectors
using the least square cross - validation (LSCV), biased cross -
validation (BCV), and direct plug -in (DPI) techniques.


Keywords


cumulative distribution function, density estimation, bandwidth, kernel method, mean square error

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