In this manuscript we discuss the effectiveness of the Kozachenko-Leonenko entropy estimator when generalised to cope with entropic forms customarily applied to study systems evincing asymptotic scale invariance and dependence (either linear or non-linear type). We show that when the variables are independently and identically distributed the estimator is only valuable along the whole domain if...

Quantiles of a random performance serve as important alternatives to the usual expected value. They are used in the financial industry as measures of risk and in the service industry as measures of service quality. To manage the quantile of a performance, we need to know how changes in the input parameters affect the output quantiles, which are called quantile sensitivities. In this paper, we s...

This paper describes and proves two important theorems that compose the Law of Large Numbers for the non-Euclidean Lp-means, known to be true for the Euclidean L2-means: Let the Lp-mean estimator, which constitutes the specific functional that estimates the Lp-mean of N independent and identically distributed random variables; then, (i) the expectation value of the Lp-mean estimator equals the ...

We describe different methods for estimating the bispectrum of Cosmic Microwave Background data. In particular we construct a minimum variance estimator for the flat-sky limit and compare results with previously-studied frequentist methods. Application to the MAXIMA dataset shows consistency with primordial Gaussianity. Weak quadratic non-Gaussianity is characterised by a tunable parameter fNL,...

The goal of this work is to study the asymptotic and finite sample properties of an estimator of a nonlinear regression function when errors are spatially correlated, and when the spatial dependence structure is unknown. The proposed method is based on a weighted nonlinear least squares approach, taking into account the spatial covariance. Weak consistency of the regression parameters estimator...

Sometimes the quality of a process or product is described by a functional relationship between a response variable and one or more explanatory variables referred to as profile. In most researches in this area the response variable is assumed to be normally distributed; however, occasionally in certain applications, the normality assumption is violated. In these cases the Generalized Linear Mod...

In the present article, motivated by Jeelani et al. (2013), we have made an attempt to develop an improved ratio type estimator of population mean using predictive method of estimation by using linear combination of coefficient of skewness and the quartile deviation of auxiliary variable. The mathematical expressions for the bias and mean squared error (MSE) of the proposed estimator up to the ...

In this Brief Report we discuss the effectiveness of the Kozachenko-Leonenko entropy estimator when generalized to cope with entropic forms customarily applied to study systems evincing asymptotic scale invariance and dependence (either of linear or nonlinear kind). We show that when the variables are independently and identically distributed the estimator is only valuable along the whole domai...

This paper deals with the problem of estimating the Multivariate version of the Conditional-TailExpectation introduced in the bivariate framework in Di Bernardino et al. (2013), and generalized in Cousin and Di Bernardino (2014). We propose a new semi-parametric estimator for this risk measure, essentially based on statistical extrapolation techniques, well designed for extreme risk levels. We ...

We formalize notions of robustness for composite estimators via the notion of a breakdown point. A composite estimator successively applies two (or more) estimators: on data decomposed into disjoint parts, it applies the first estimator on each part, then the second estimator on the outputs of the first estimator. And so on, if the composition is of more than two estimators. Informally, the bre...