Related papers: Generalized Arithmetic and Geometric Mean Divergen…
Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…
General ridge estimators are typical linear estimators in a general linear model. The class of them includes some shrinkage estimators in addition to classical linear unbiased estimators such as the ordinary least squares estimator and the…
This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the…
In these notes we generalize the notion of a (pseudo) metric measuring the distance of two points, to a (pseudo) n-metric which assigns a value to a tuple of n points. We present two principles of constructing pseudo n-metrics. The first…
We consider Gini's mean difference statistic as an alternative to the empirical variance in the settings of finite populations where simple random samples are drawn without replacement. In particular, we discuss specific (in the finite…
Generalized linear (GL-) statistics are defined as functionals of an U-quantile process and unify different classes of statistics such as U-statistics and L-statistics. We derive a central limit theorem for GL-statistics of strongly mixing…
In this article we give some improvements and generalizations of the famous Jensen's and Jensen-Mercer inequalities for twice differentiable functions, where convexity property of the target function is not assumed in advance. They…
We show that a special case of method of moment estimator derived from the Stein class coincides with the class of generalized score matching estimator. Choosing a suitable weight function for generalized score matching is not…
By using the Renyi entropy, and following the same scheme that in the Fisher-Renyi entropy product case, a generalized statistical complexity is defined. Several properties of it, including inequalities and lower and upper bounds are…
Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…
In this paper we introduce the concepts of p-logarithmic and Alpha-power divergence measures and point out a number of basic results.
We introduce a distance in the space of fully-supported probability measures on one-dimensional symbolic spaces. We compare this distance to the $\bar{d}$-distance and we prove that in general they are not comparable. Our projective…
It is argued that every measurement is made in a certain scale. The scale in which present measuments are made is called present scale which gives present knowledge. Quantities at the limits to present measurement may be observables in…
Gauss's arithmetic-geometric mean (AGM) which is described by two variables iteration $(a_n, b_n)\rightarrow (a_{n+1}, b_{n+1})$ by $a_{n+1}=(a_n+b_n)/2,\ b_{n+1}=\sqrt{a_nb_n}$. We extend it to three variables iteration $(a_n, b_n,…
By establishing a connection between bi-directional Helmholtz machines and information theory, we propose a generalized Helmholtz machine. Theoretical and experimental results show that given \textit{shallow} architectures, the generalized…
When averages of different experimental determinations of the same quantity are computed, each with statistical and systematic error components, then frequently the statistical and systematic components of the combined error are quoted…
The aims of this letter are two. First, to show the angular gauge-invariance on the response of interferometers to gravitational waves (GWs). In this process, after resuming for completeness results on the Transverse-Traceless (TT) gauge,…
This paper is an attempt to set a justification for making use of some dicrepancy indexes, starting from the classical Maximum Likelihood definition, and adapting the corresponding basic principle of inference to situations where…
The Gini's mean difference was defined as the expected absolute difference between a random variable and its independent copy. The corresponding normalized version, namely Gini's index, denotes two times the area between the egalitarian…
Measurement incompatibility stipulates the existence of quantum measurements that cannot be carried out simultaneously on single systems. We show that the set of input-output probabilities obtained from d-dimensional classical systems…