Related papers: Uniform-in-bandwidth consistency for kernel-type e…
We present a numerical study of the application of the Shannon entropy technique to the planar restricted three-body problem in the vicinity of first-order interior mean-motion resonances with the perturber. We estimate the diffusion…
One of the main problems in cryptography is to give criteria to provide good comparators of cipher systems. The security of a cipher system must include the security of the algorithm, the security of the key generator and management module…
A class of estimators of the R\'{e}nyi and Tsallis entropies of an unknown distribution $f$ in $\mathbb{R}^m$ is presented. These estimators are based on the $k$th nearest-neighbor distances computed from a sample of $N$ i.i.d. vectors with…
In the spatial point process context, kernel intensity estimation has been mainly restricted to exploratory analysis due to its lack of consistency. Different methods have been analysed to overcome this problem, and the inclusion of…
Kernel-based nonparametric hazard rate estimation is considered with a special class of infinite-order kernels that achieves favorable bias and mean square error properties. A fully automatic and adaptive implementation of a density and…
We consider nonparametric estimation of the derivative of a probability density function with the bounded support on $[0,\infty)$. Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma…
Estimating entropies from limited data series is known to be a non-trivial task. Naive estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals Shannon,…
Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…
We determine the amount of information contained in a time series of price returns at a given time scale, by using a widespread tool of the information theory, namely the Shannon entropy, applied to a symbolic representation of this time…
We prove a variety of new and refined uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimensional systems. We obtain the first tight continuity estimate…
This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…
In this paper, the regularity results for the integro-differential operators of the fractional Laplacian type by Caffarelli and Silvestre \cite{CS1} are extended to those for the integro-differential operators associated with symmetric,…
Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled…
In this article, basing on NQD samples, we investigate the fixed design nonparametric regression model, where the errors are pairwise NQD random errors, with fixed design points, and an unknown function. Nonparametric weighted estimator…
This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya-Watson kernel regression, and local linear estimation. Our…
There is an intense and partly recent literature focussing on the problem of selecting the bandwidth parameter for kernel density estimators. Available methods are largely `very nonparametric', in the sense of not requiring any knowledge…
We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…
We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…
A thermodynamic framework for asymptotic inference is developed in which sample size and parameter variance define a state space. Within this description, Shannon information plays the role of entropy, and an integrating factor organizes…
Uncertainty relations lie at the very core of quantum mechanics, and form the cornerstone of essentially all quantum cryptographic applications. In particular, they play an important role in cryptographic protocols in the…