Stable Nonparametric Signal Filtration in Nonlinear Models

Dobrovidov, A. V.

doi:10.1007/978-1-4939-0569-0_7

Cited by 3 publications

(1 citation statement)

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“…The pdf derivative estimation have practical use in an optimal filtering in signal processing and control of nonlinear processes where only the exponential pdf class is used (cf. Dobrovidov et al (2012); Dobrovidov and Koshkin (2011)). For more details see Sec.…”

Section: Practical Motivationmentioning

confidence: 99%

Nonparametric Estimation of Multivariate Density and its Derivative by Dependent Data Using Gamma Kernels

Markovich

2021

J Math Sci

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We consider the nonparametric estimation of the multivariate probability density function and its partial derivative with a support on [0, ∞) by dependent data. To this end we use the class of kernel estimators with asymmetric gamma kernel functions. The gamma kernels are nonnegative. They change their shape depending on the position on the semi-axis and possess good boundary properties for a wide class of densities. The theoretical asymptotic properties of the multivariate density and its partial derivative estimates like biases, variances and covariances are derived. We obtain the optimal bandwidth selection for both estimates as a minimum of the mean integrated squared error (MISE) assuming dependent data with a strong mixing. Optimal rates of convergence of the MISE both for the density and its derivative are found.

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Section: Practical Motivationmentioning

confidence: 99%