Generalised gamma kernel density estimation for nonnegative data and its bias reduction

We consider density estimation for nonnegative data using generalised gamma density. What is being emphasised here is that a negative exponent is allowed. We show that, for each positive or negative exponent, (i) generalised gamma kernel density estimator, without bias reduction, has the mean integr...

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Bibliographic Details
Published in:Journal of nonparametric statistics 2018-07, Vol.30 (3), p.598-639
Main Authors: Igarashi, Gaku, Kakizawa, Yoshihide
Format: Article
Language:English
Subjects:
asymmetric kernel
Bias
boundary bias problem
Density
Estimators
generalised gamma (or Amoroso) kernel
Nonparametric density estimator
Nonparametric statistics
Reduction
Sample size
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Summary:We consider density estimation for nonnegative data using generalised gamma density. What is being emphasised here is that a negative exponent is allowed. We show that, for each positive or negative exponent, (i) generalised gamma kernel density estimator, without bias reduction, has the mean integrated squared error (MISE) of order , as in other boundary-bias-free density estimators from the existing literature, and that (ii) the bias-reduced versions have the MISEs of order , where n is the sample size. We illustrate the finite sample performance of the proposed estimators through the simulations.
ISSN:1048-5252
1029-0311
DOI:10.1080/10485252.2018.1457791