Abstract – Nonparametric density estimation is considered for a discretely observed stationary continuous-time process. For each of three given time sampling procedures either random or deterministic, we establish that histograms and frequency polygons can reach the same optimal L2-rates as in the independent and identically distributed case. Moreover, thanks to a suitable “high frequency” samp...

Finding models for linear-time properties is a central problem in verification and planning. We study the distribution of lineartime models by investigating the density of linear-time properties over the space of ultimately periodic words. The density of a property over a bound n is the ratio of the number of lasso-shaped words of length n, that satisfy the property, to the total number of lass...

We develop a wavelet based linear density estimator for the estimation of the probability density function for a sequence of associated random variables with a common onedimensional probability density function and obtain bounds on Lp-losses for such estimators.

A nonparametric kernel density estimator for directional–linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions for bias, variance and mean integrated square error (MISE) are derived, jointly with an asymptotic normality result for the proposed estimator. For some part...

For linear regression models with non-normally distributed errors, the least squares estimate (LSE) will lose some efficiency compared to the maximum likelihood estimate (MLE). In this article, we propose a kernel density based regression estimate (KDRE) that is adaptive to the unknown error distribution. The key idea is to approximate the likelihood function by using a nonparametric kernel den...

We discuss a couple of simple quasistatic electromagnetic systems in which the density of electromagnetic linear momentum can be easily computed. The examples are also used to illustrate how the total electromagnetic linear momentum, which may also be calculated by using the vector potential, can be understood as a consequence of the violation of the action–reaction principle, because a non-nul...

ABSTRACT The stationary density of a centered invertible linear processes can be represented as a convolution of innovation-based densities, and it can be estimated at the parametric rate by plugging residual-based kernel estimators into the convolution representation. We have shown elsewhere that a functional central limit theorem holds both in the space of continuous functions vanishing at in...

We study the problem of learning the best linear and convex combination of M estimators of a density with respect to the mean squared risk. We suggest aggregation procedures and we prove sharp oracle inequalities for their risks, i.e., oracle inequalities with leading constant 1. We also obtain lower bounds showing that these procedures attain optimal rates of aggregation. As an example, we con...