Bayesian selector of adaptive bandwidth for multivariate gamma kernel estimator on [0,∞ ) ^d

Bayesian bandwidth selections in multivariate associated kernel estimation of probability density functions are known to improve classical methods such as cross-validation techniques in terms of execution time and smoothing quality. The paper focuses on a basic multivariate gamma kernel which is appropriated to estimate densities with support $[0,\infty {)}^d$ . For this purpose, we consider a Bayesian adaptive estimation of the bandwidths vector under the usual quadratic loss function. The exact expression of the posterior distribution and the vector of bandwidths are obtained. Simulations studies highlight the excellent performance of the proposed approach, comparing to the global cross-validation bandwidth selection, and under integrated squared errors. Two bivariate and trivariate applications to the Old Faithful geyser data and new ones on drinking water pumps in the Sahel, respectively, are made.