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Relative efficiency and deficiency of kernel type estimators of smooth distribution functions
Author(s) -
Falk M.
Publication year - 1983
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1983.tb00802.x
Subject(s) - mathematics , estimator , kernel (algebra) , empirical distribution function , type (biology) , efficiency , distribution (mathematics) , function (biology) , mathematical optimization , statistics , combinatorics , mathematical analysis , evolutionary biology , ecology , biology
Abstract The problem is investigated whether a given kernel type estimator of a distribution function at a single point has asymptotically better performance than the empirical estimator. A representation of the relative deficiency of the empirical distribution function with respect to a kernel type estimator is established which gives a complete solution to this problem. The problem of finding optimal kernels is studied in detail.