A class of R-estimators based on the concepts of multivariate signed ranks and the optimal rank-based tests developed in Hallin and Paindaveine [Ann. Statist. 34 (2006)] is proposed for the estimation of the shape matrix of an elliptical distribution. These R-estimators are root-n consistent under any radial density g, without any moment assumptions, and semiparametrically efficient at some pre...

Squeezed states are characterized by a phasedependent redistribution of quantum fluctuations such that the dispersion in one of the two quadrature components of the field is reduced below the level set by the symmetric distribution of the vacuum state or a coherent state [1]. Such a property has been used to raise the sensitivity beyond the standard quantum limit [2, 3] and to enhance interfero...

by shouldering the burden of a big chunk of global production, and giving shelter to half of the world’s population, currently cities play an important role in national economies. benefits of agglomeration in cities have played a major role in the process of economic development of different countries, however, the expansion of urbanization has produced some problems including environmental and...

Let u(x) = s(x) + n(x) , where s(x) and n(x) are random fields, s(x) is useful signal, n(x) is noise. Assume that s(x) = n(x) = 0 , where the bar stands for mean value. Suppose that the covariance functions R(x, y) := u * (x)u(y) and f (x, y) := u * (x)s(y) are known, where the asterisk stands for complex conjugate. Assume that u(x) is observed in a bounded domain D ⊂ R r of the Euclidean space...

The problem of nonparametric function estimation has received a substantial amount of attention in the statistical literature over the last 15 years. To a very large extent, the literature has described kernel-based convolution smoothing solutions to the problems of probability density estimation and nonlinear regression. Among the subcultures within this literature has been a substantial effor...

In statistics, the univariate kernel density estimation (KDE) is a non-parametric way to estimate the probability density function f(x) of a random variable X, is a fundamental data smoothing problem where inferences about the population are made, based on a finite data sample. This techniques are widely used in various inference procedures such as signal processing, data mining and econometric...