Abstract:
We introduce a new class of nonparametric density estimators. It includes the classical kernel density estimator as well as the popular Abramson's estimator. We show that generalized estimators may perform much better than the classical one if the distribution has a heavy tail. The asymptotics of the mean squared error (MSE), optimal (in a sense) kernel, and smoothing parameter are found.
This publication is cited in the following 6 articles:
Nakarmi J. Sang H. Ge L., “Variable Bandwidth Kernel Regression Estimation”, ESAIM-Prob. Stat., 25 (2021), 55–86
Nakarmi J., Sang H., “Central Limit Theorem For the Variable Bandwidth Kernel Density Estimators”, J. Korean Stat. Soc., 47:2 (2018), 201–215
Gine E., Sang H., “Uniform asymptotics for kernel density estimators with variable bandwidths”, Journal of Nonparametric Statistics, 22:6 (2010), 773–795
Novak S.Y., “Impossibility of consistent estimation of the distribution function of a sample maximum”, Statistics, 44:1 (2010), 25–30
S. Y. Novak, “Lower bounds to the accuracy of sample maximum estimation”, Theory Stoch. Process., 15(31):2 (2009), 156–161
N. M. Markovich, “Accuracy of transformed kernel density estimates for a heavy-tailed distribution”, Autom. Remote Control, 66:2 (2005), 217–232
Citation in format AMSBIB
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