A Class of Nonparametric Density Derivative Estimators Based on Global Lipschitz Conditions

Kairat Mynbaev, Carlos Martins-Filho and Aziza Aipenova

A chapter in Essays in Honor of Aman Ullah, 2016, vol. 36, pp 591-615 from Emerald Group Publishing Limited

Abstract: Estimators for derivatives associated with a density function can be useful in identifying its modes and inflection points. In addition, these estimators play an important role in plug-in methods associated with bandwidth selection in nonparametric kernel density estimation. In this paper, we extend the nonparametric class of density estimators proposed by Mynbaev and Martins-Filho (2010) to the estimation ofm-order density derivatives. Contrary to some existing derivative estimators, the estimators in our proposed class have a full asymptotic characterization, including uniform consistency and asymptotic normality. An expression for the bandwidth that minimizes an asymptotic approximation for the estimators’ integrated squared error is provided. A Monte Carlo study sheds light on the finite sample performance of our estimators and contrasts it with that of density derivative estimators based on the classical Rosenblatt–Parzen approach.

Keywords: Nonparametric derivative estimation; Lipschitz conditions; 62G07; 62G20; C14; C18 (search for similar items in EconPapers)
Date: 2016
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Related works:
Working Paper: A class of nonparametric density derivative estimators based on global Lipschitz conditions (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:eme:aecozz:s0731-905320160000036026

DOI: 10.1108/S0731-905320160000036026

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