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

* The authors preliminarily reported some asymptotic results, at the Japanese Joint Statistical Meeting (2016, September).

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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.