Smoothing Counting Process Intensities by Means of Kernel Functions

Integral approximation by kernel smoothing

where f̂ is the classical kernel estimator of the density of X1. This result is striking because it speeds up traditional rates, in root n, derived from the central limit theorem when f̂ = f . Although this paper highlights some applications, we mainly address theoretical issues related to the later result. We derive upper bounds for the rate of convergence in probability. These bounds depend on ...

Smoothing by Spline Functions

On the Means of the Values of Prime Counting Function

In this paper, we investigate the means of the values of prime counting function $pi(x)$. First, we compute the arithmetic, the geometric, and the harmonic means of the values of this function, and then we study the limit value of the ratio of them.

Multistep kernel regression smoothing by boosting

In this paper we propose a simple multistep regression smoother which is constructed in a boosting fashion, by learning the Nadaraya–Watson estimator with L2Boosting. Differently from the usual approach, we do not focus on L2Boosting for ever. Given a kernel smoother as a learner, we explore the boosting capability to build estimators using a finite number of boosting iterations. This approach ...

Local Self-concordance of Barrier Functions Based on Kernel-functions

 Many efficient interior-point methods (IPMs) are based on the use of a self-concordant barrier function for the domain of the problem that has to be solved. Recently, a wide class of new barrier functions has been introduced in which the functions are not self-concordant, but despite this fact give rise to efficient IPMs. Here, we introduce the notion of locally self-concordant barrier functio...