On the kernel selection for minimum-entropy estimation

A Statistical Inference Comparison for Measurement Estimation Using Stochastic Simulation Techniques

“…This section illustrates another proposed approach which is based on the Minimum-Entropy Estimation (MEE) concepts and the simultaneous use of the bootstrap simulation methods [6], [7] (as seen in § IV-A). The final objective is the same, to obtain a complete statistical characterization of the MEE parameter estimators and d and l estimators.…”

“…In cases where limited information is available, the most natural proposition is to take a small number of hypotheses and take advantage of all information contained in the data itself using methods like the bootstrap (parametric or non-parametric) [15]- [17], [19]- [22], [39], [40], the kernel methods or non-parametric estimation [6]- [9], and all related methods [1], [11]- [14], [27], [28], [37] (see also some research work of Parzen-Rosenblatt dating of 1968).…”

MAP entropy estimation: applications in robust image filtering

“…Our proposition for a new MAP scheme is to use a Generalized Gaussian MRF introduced by Bouman and Sauer in [4,7], together with three kernel estimators used in [8,9], and [10] to obtain cost functionals or criterions based on the entropy of the approximated likelihood function (first term of Eq. (3)) p n,h (e).…”

“…K h (e − e i ) . (8) This expression assumes the hypothesis that p(e) is symmetric, two times differentiable and positive, indeed, it is assumed that K(•) is a kernel weighted function which satisfies some imposed conditions treated in the work of Masry [18] and subsequently taken back by Devroye [19]- [22], Berlinet [23], and Loader [24] in some of their research work. The bandwidth h = h n is given in function of the sample size n, this parameter could be considered as a sequence of positive numbers that must satisfy: h n → 0 and nh n → ∞ when n → ∞.…”

“…The image modeling in the context of the present paper lead us to assume a limited knowledge about the image noise pdf (see Eq. (3), where p(e) = p(y|x)), so we propose to use the data itself to obtain a non-parametric Entropy Estimate (EE) of the log-likelihood pdf ( p n,h (e)) [8]- [10], similar methodologies have been proposed in recent works by Milanfar et al, [11,12]. Then the log-likelihood will be optimized together with a log-MRF to obtain the MAP image estimation.…”