 Mise of kernel estimates of a density and its derivativesRadhey S. Singh Statistics & Probability Letters, 1987, vol. 5, issue 2, 153-159 Abstract: For an integer p [greater-or-equal, slanted] 0, Singh has considered a class of kernel estimators [latin small letter f with hook]~(p) of the pth order derivative [latin small letter f with hook](p) of a density [latin small letter f with hook] and showed how specializations of some of the results there improve the corresponding existing results. In this paper these improved estimators are examined on a global measure of quality of an estimator, namely, the mean integrated square error (MISE) behavior. An upper bound, which can not be tightened any further for a wide class of kernels, is obtained for MISE ([latin small letter f with hook]~(p)). The exact asymptotic value for the same is also obtained. Under two alternative conditions, weaker than those assumed for the two results mentioned above, convergence of MISE ([latin small letter f with hook]~(p)) to zero is proved. Specializations of some of the results here improve the corresponding existing results by weakening the conditions, sharpening the rates of convergence or both. Keywords: estimates; density; derivatives; of; a; density; mean; integrated; square; error; asymptotic; behavior (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:5:y:1987:i:2:p:153-159 Ordering information: This journal article can be ordered from Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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