In this paper, we consider the problem of estimating the covariance kernel and its eigenvalues and eigenfunctions from sparse, irregularly observed, noise corrupted and (possibly) correlated functional data. We present a method based on pre-smoothing of individual sample curves through an appropriate kernel. We show that the naive empirical covariance of the pre-smoothed sample curves gives hig...

Abstract. In this paper we, firstly, present a recursive formula of the empirical estimator of the semi-Markov kernel. Then a non-parametric estimator of the expected cumulative operational time for semi-Markov systems is proposed. The asymptotic properties of this estimator, as the uniform strongly consistency and normality are given. As an illustration example, we give a numerical application.

-We develop a method of performing pattern recognition (discrimination and classification) using a recursive technique derived from mixture models, kernel estimation and stochastic approximation. Unsupervised learning Density estimation Kernel estimator Mixture model Stochastic approximation Recursive estimation

We introduce a new two-step kernel density estimation method, based on the EM algorithm and the generalized kernel density estimator. The accuracy obtained is better in particular, in the case of multimodal or skewed densities.

Estimating an unknown probability density function is a common problem arising frequently in many scientific disciplines. Among many density estimation methods, the kernel density estimators are widely used. However, the classical kernel density estimators suffer from an intrinsic problem as they assign positive values outside the support of the target density. This problem is commonly known as...

Abstract. Semiparametric model is a statistical model consisting of both parametric and nonparametric components, which can be looked on as a mixture model. The theoretical properties of this model have been studied extensively, such as large-sample property. However, most researches are based on scalar value, in which the dimension of the observation is one at each moment. In the fields of spa...

Generally, blind separation of sources from their nonlinear mixtures is rather difficult. This nonlinear mapping, constituted by unsupervised linear mixing followed by unknown and invertible nonlinear distortion, is found in many signal processing cases. We propose using a kernel density estimator incorporated within an equivariant gradient algorithm to separate the nonlinear mixed sources. The...

We establish the asymptotical equivalence between L-spline smoothing and kernel estimation. The equivalent kernel is used to derive the asymptotic mean squared error of the L-smoothing spline estimator. The paper extends the corresponding results for polynomial spline smoothing.

Often times there is a need to infer the true underlying probability based on the observations, such as in, including but not limited to, data-mining, optimizing the process control parameters etc., Histograms, very rudimentary empirical density estimators, divide the whole data range into either equal or unequal sub intervals (bins) and then obtain the frequency of occurrence of each bin. They...

We consider functional measurement error models where the measurement error distribution is estimated non-parametrically.We derive a locally efficient semiparametric estimator but propose not to implement it owing to its numerical complexity. Instead, a plug-in estimator is proposed, where the measurement error distribution is estimated through non-parametric kernel methods based on multiple me...