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Correction of Density Estimators that are not Densities
Author(s) -
Glad Ingrid K.,
Hjort Nils Lid,
Ushakov Nikolai G.
Publication year - 2003
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 - 10.1111/1467-9469.00339
Subject(s) - estimator , mathematics , kernel density estimation , sinc function , extremum estimator , multivariate kernel density estimation , bootstrapping (finance) , kernel (algebra) , m estimator , set (abstract data type) , parametric statistics , invariant estimator , statistics , variable kernel density estimation , minimum variance unbiased estimator , econometrics , kernel method , minimax estimator , computer science , artificial intelligence , mathematical analysis , combinatorics , support vector machine , programming language
Abstract. Several old and new density estimators may have good theoretical performance, but are hampered by not being bona fide densities; they may be negative in certain regions or may not integrate to 1. One can therefore not simulate from them, for example. This paper develops general modification methods that turn any density estimator into one which is a bona fide density, and which is always better in performance under one set of conditions and arbitrarily close in performance under a complementary set of conditions. This improvement‐for‐free procedure can, in particular, be applied for higher‐order kernel estimators, classes of modern h 4 bias kernel type estimators, superkernel estimators, the sinc kernel estimator, the k ‐NN estimator, orthogonal expansion estimators, and for various recently developed semi‐parametric density estimators.