In this paper, we consider an interesting problem on adaptive Birnbaum-Saunders-power-exponential (BS-PE) kernel density estimation for nonnegative heavy-tailed (HT) data. Treating the variable bandwidths h i , i = 1, . . . , n of adaptive BS-PE kernel as parameters, we then propose a conjugate prior and estimate the h i 's by using the popular quadratic and entropy loss functions. Explicit formulas are obtained for the posterior and Bayes estimators. Comparison simulations with global unbiased cross-validation bandwidth selection technique were conducted under four HT distributions. Finally, two applications based on HT real data are presented and analyzed.
In this paper, we consider the procedure for deriving variable bandwidth in univariate kernel density estimation for nonnegative heavy-tailed (HT) data.
These procedures consider the Birnbaum–Saunders power-exponential (BS-PE) kernel estimator and the bayesian approach that treats the adaptive bandwidths.
We adapt an algorithm that subdivides the HT data set into two regions, high density region (HDR) and low-density region (LDR), and we assign a bandwidth parameter for each region.
They are derived by using a Monte Carlo Markov chain (MCMC) sampling algorithm.
A series of simulation studies and real data are realized for evaluating the performance of a procedure proposed.
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