A symmetrization technique for continuous-variable quantum key distribution

We introduce a symmetrization technique which can be used as an extra step in some continuous-variable quantum key distribution protocols. By randomizing the data in phase space, one can dramatically simplify the security analysis of the protocols, in particular in the case of collective attacks. The main application of this procedure concerns protocols with postselection, for which security was established only against Gaussian attacks until now. Here, we prove that under some experimentally verifiable conditions, Gaussian attacks are optimal among all collective attacks.Comment: 7 page

Strong laws for generalized absolute Lorenz curves when data are stationary and ergodic sequences

We consider generalized absolute Lorenz curves that include, as special cases, classical and generalized L - statistics as well as absolute or, in other words, generalized Lorenz curves. The curves are based on strictly stationary and ergodic sequences of random variables. Most of the previous results were obtained under the additional assumption that the sequences are weakly Bernoullian or, in other words, absolutely regular. We also argue that the latter assumption can be undesirable from the applications point of vie

Background Risk Models and Stepwise Portfolio Construction

Assuming the multiplicative background risk model, which has been a popular model due to its practical applicability and technical tractability, we develop a general framework for analyzing portfolio performance based on its subportfolios. Since the performance of subportfolios is easier to assess, the herein developed stepwise portfolio construction (SPC) provides a powerful alternative to a number of traditional portfolio construction methods. Within this framework, we discuss a number of multivariate risk models that appear in the actuarial and financial literature. We provide numerical and graphical examples that illustrate the SPC technique and facilitate our understanding of the herein developed general results

On estimation of Poisson intensity functions

Under the presence of only one realization, we consider a computationally simple algorithm for estimating the intensity function of a Poisson process with exponential quadratic and cyclic of fixed frequency trends. We argue that the algorithm can successfully be used to estimate any Poisson intensity function provided that it has a parametric form

Consistent estimation of the intensity function of a cyclic Poisson process

We construct and investigate a consistent kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process when the period is unknown. We assume that only a single realization of the Poisson process is observed in a bounded window. In particular, we prove that the proposed estimator is weakly and strongly consistent when the size of the window expands

A non-parametric estimator for the doubly-periodic Poisson intensity function

In a series of papers, J. Garrido and Y. Lu have proposed and investigated a doubly-periodic Poisson model, and then applied it to analyze hurricane data. The authors have suggested several parametric models for the underlying intensity function. In the present paper we construct and analyze a non-parametric estimator for the doubly-periodic intensity function. Assuming that only a single realization of the process is available in a bounded window, we show that the estimator is consistent and asymptotically normal when the window expands indefinitely. In addition we calculate the asymptotic bias and variance of the estimator, and in this way gain helpful information for optimizing the performance of the estimator

Statistical properties of a kernel type estimator of the intensity function of a cyclic poisson process

We consider a kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process when the period is unknown. We assume that only a single realization of the Poisson process is observed in a bounded window which expands in time. We compute the asymptotic bias, variance, and the mean squared error of the estimator when the window indefinitely expands

Weak convergence of Vervaat and Vervaat Error processes of long-range dependent sequences

Following Cs\"{o}rg\H{o}, Szyszkowicz and Wang (Ann. Statist. {\bf 34}, (2006), 1013--1044) we consider a long range dependent linear sequence. We prove weak convergence of the uniform Vervaat and the uniform Vervaat error processes, extending their results to distributions with unbounded support and removing normality assumption