Minimum-entropy, PDF approximation, and kernel selection for measurement estimation

The purpose of this paper is to investigate the selection of an appropriate kernel to be used in a recent robust approach called minimum-entropy estimator (MEE). This MEE estimator is extended to measurement estimation and pdf approximation when ρ(e) is unknown. The entropy criterion is constructed on the basis of a symmetrized kernel estimate ρ_n,h(e) of ρ(e). The MEE performance is generally better than the Maximum Likelihood (ML) estimator. The bandwidth selection procedure is a crucial task to assure consistency of kernel estimates. Moreover, recent proposed Hilbert kernels avoid the use of bandwidth, improving the consistency of the kernel estimate. A comparison between results obtained with normal, cosine and Hilbert kernels is presented.