A plugin heuristic for probability density function estimator adapted to complex shape distribution

A non-parametric estimator of the probability density by the histogram or the kernel method depends upon the so called smoothing parameter h, also called bandwidth or sometimes bin-width. The choice is crucial for the accuracy of the estimator. It usually based on specific convergence theorems. In this work, we propose to compare the most efficient methods in the literature for the selection of this parameter such as the Cross Validation and Rule Of Thumb family of methods. Thus, we proposed a new algorithm of selection of bin-width for the method of the histogram which we call it “Plugin histogram” It consists to an iterative procedure based on the solution of the optimization of the MISE. It gives encouraging results essentially in the case of the multimodal distributions and for the distributions with bounded support.