Open AccessThe Generalised Plug-in Algorithm for the Diffeomorphism Kernel Estimate
Author(s) -
M. Troudi,
Faouzi Ghorbel
Publication year - 2021
Publication title -
international journal of mathematics and computers in simulation
Language(s) - English
Resource type - Journals
ISSN - 1998-0159
DOI - 10.46300/9102.2021.15.24
Subject(s) - bounded function , estimator , mathematics , smoothing , kernel (algebra) , kernel smoother , algorithm , diffeomorphism , variable kernel density estimation , mathematical optimization , kernel method , computer science , statistics , support vector machine , artificial intelligence , discrete mathematics , mathematical analysis , radial basis function kernel
The optimal value of the smoothing parameter of the Kernel estimator can be obtained by the well known Plug-in algorithm. The optimality is realised in the sense of Mean Integrated Square Error (MISE). In this paper, we propose to generalise this algorithm to the case of the difficult problem of the estimation of a distribution which has a bounded support. The proposed algorithm consists in searching the optimal smoothing parameter by iterations from the expression of MISE of the kernel-diffeomorphism estimator. By some simulations applied to some distribution having a support bounded and semi bounded, we show that the support of the pdf estimator respects the one of the theoretical distribution. We also prove that the proposed method minimizes the Gibbs phenomenon.