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A New Kernel Distribution Function Estimator Based on a Non‐parametric Transformation of the Data
Author(s) -
SWANEPOEL JAN W. H.,
VAN GRAAN FRANCOIS C.
Publication year - 2005
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2005.00472.x
Subject(s) - mathematics , estimator , efficient estimator , mean squared error , kernel (algebra) , kernel density estimation , statistics , invariant estimator , bias of an estimator , kernel smoother , consistent estimator , parametric statistics , minimum variance unbiased estimator , kernel method , computer science , artificial intelligence , combinatorics , radial basis function kernel , support vector machine
. A new kernel distribution function (df) estimator based on a non‐parametric transformation of the data is proposed. It is shown that the asymptotic bias and mean squared error of the estimator are considerably smaller than that of the standard kernel df estimator. For the practical implementation of the new estimator a data‐based choice of the bandwidth is proposed. Two possible areas of application are the non‐parametric smoothed bootstrap and survival analysis. In the latter case new estimators for the survival function and the mean residual life function are derived.