Fourier methods for smooth distribution function estimation

In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the distribution and the Fourier transform of the kernel are employed to obtain the limit value of the optimal bandwidth sequence in its greatest generality. The assumptions in our results are mild enough so that they are applicable when the kernel used in the estimator is a superkernel, or even the sinc kernel, and this allows to extract some interesting consequences, as the existence of a class of distributions for which the kernel estimator achieves a first-order improvement in efficiency over the empirical distribution function.Comment: 12 pages, 2 figure

Modal clustering asymptotics with applications to bandwidth selection

Density-based clustering relies on the idea of linking groups to some specific features of the probability distribution underlying the data. The reference to a true, yet unknown, population structure allows to frame the clustering problem in a standard inferential setting, where the concept of ideal population clustering is defined as the partition induced by the true density function. The nonparametric formulation of this approach, known as modal clustering, draws a correspondence between the groups and the domains of attraction of the density modes. Operationally, a nonparametric density estimate is required and a proper selection of the amount of smoothing, governing the shape of the density and hence possibly the modal structure, is crucial to identify the final partition. In this work, we address the issue of density estimation for modal clustering from an asymptotic perspective. A natural and easy to interpret metric to measure the distance between density-based partitions is discussed, its asymptotic approximation explored, and employed to study the problem of bandwidth selection for nonparametric modal clustering

Lithogeochemistry and fluid flow in the epithermal Veta Rublo base metal-silver deposit, Chonta Mine (Huancavelica, Perú)

The Chonta Mine (75º00’30” W & 13º04’30”S, 4495 to 5000 m absl), owned by Compañía Minera Caudalosa, operates a polymetallic Zn-Pb-Cu-Ag vein system of the low sulphidation epithermal type, hosted by cenozoic volcanics of dacitic to andesitic composition (Domos de Lava Formation). Veta Rublo, one of the main veins of the system, is worked underground to nearly 300 m. It strikes 60-80º NE and dips 60-70º SE; its width varies between 0.30 and 2.20m, and it crops out along 1 km, but is continued along strike by other veins, as Veta Caudalosa, for some 5 km. Typical metal contents are 7% Zn, 5% Pb, 0.4% Cu and 3 oz/t Ag, with quartz, sericite, sphalerite, galena, pyrite, chalcopyrite, fahlore as main minerals, and minor carbonate and sulphosalts