The estimation of density functions for positive multivariate data is discussed. The proposed approach is semiparametric. The estimator combines gamma kernels or local linear kernels, also called boundary kernels, for the estimation of the marginal densities with parametric copulas to model the...

We consider the smoothed histograms by gamma densities for an i.i.d. sample defined on the positive real line. Under sufficient conditions on the bandwidth and the density function, we obtain the asymptotic behavior, the lower and upper bound of the expected average absolute error of this...

We consider asymmetric kernel density estimators and smoothed histogramswhen the unknown probability density function f is defined on [0, +∞). Uniform weak consistency on each compact set in [0, +∞) is proved for these estimators when "f" is continuous on its support. Weak convergence in L...