Search results for "order statistics"

An Analysis of Earthquakes Clustering Based on a Second-Order Diagnostic Approach

2009

A diagnostic method for space–time point process is here introduced and applied to seismic data of a fixed area of Japan. Nonparametric methods are used to estimate the intensity function of a particular space–time point process and on the basis of the proposed diagnostic method, second-order features of data are analyzed: this approach seems to be useful to interpret space–time variations of the observed seismic activity and to focus on its clustering features.

Some properties of local weighted second-order statistics for spatio-temporal point processes

2019

Diagnostics of goodness-of-fit in the theory of point processes are often considered through the transformation of data into residuals as a result of a thinning or a rescaling procedure. We alternatively consider here second-order statistics coming from weighted measures. Motivated by Adelfio and Schoenberg (Ann Inst Stat Math 61(4):929–948, 2009) for the temporal and spatial cases, we consider an extension to the spatio-temporal context in addition to focussing on local characteristics. In particular, our proposed method assesses goodness-of-fit of spatio-temporal models by using local weighted second-order statistics, computed after weighting the contribution of each observed point by the…

The fundamental theory of optimal "Anti-Bayesian" parametric pattern classification using order statistics criteria

2013

Author's version of an article in the journal: Pattern Recognition. Also available from the publisher at: http://dx.doi.org/10.1016/j.patcog.2012.07.004 The gold standard for a classifier is the condition of optimality attained by the Bayesian classifier. Within a Bayesian paradigm, if we are allowed to compare the testing sample with only a single point in the feature space from each class, the optimal Bayesian strategy would be to achieve this based on the (Mahalanobis) distance from the corresponding means. The reader should observe that, in this context, the mean, in one sense, is the most central point in the respective distribution. In this paper, we shall show that we can obtain opti…

Higher order statistics of the response of MDOF linear systems excited by linearly parametric white noises and external excitations

1997

The aim of this paper is the evaluation of higher order statistics of the response of linear systems subjected to external excitations and to linearly parametric white noise. The external excitations considered are deterministic or filtered white noise processes. The procedure implies the knowledge of the transition matrix connected to the linear system; this, however, has already been evaluated for obtaining the statistics at single times. The method, which avoids making further integrations for the evaluation of the higher order statistics, is very advantageous from a computational point of view.

Higher order statistics of the response of MDOF linear systems under polynomials of filtered normal white noises

1997

This paper exploits the work presented in the companion paper in order to evaluate the higher order statistics of the response of linear systems excited by polynomials of filtered normal processes. In fact, by means of a variable transformation, the original system is replaced by a linear one excited by external and linearly parametric white noise excitations. The transition matrix of the new enlarged system is obtained simply once the transition matrices of the original system and of the filter are evaluated. The method is then applied in order to evaluate the higher order statistics of the approximate response of nonlinear systems to which the pseudo-force method is applied.

Higher order statistics of the response of linear systems excited by polynomials of filtered Poisson pulses

1999

The higher order statistics of the response of linear systems excited by polynomials of filtered Poisson pulses are evaluated by means of knowledge of the first order statistics and without any further integration. This is made possible by a coordinate transformation which replaces the original system by a quasi-linear one with parametric Poisson delta-correlated input; and, for these systems, a simple relationship between first order and higher order statistics is found in which the transition matrix of the dynamical new system, incremented by the correction terms necessary to apply the Ito calculus, appears.

Diagnostics for nonparametric estimation in space-time seismic processes

2010

In this paper we propose a nonparametric method, based on locally variable bandwidths kernel estimators, to describe the space-time variation of seismic activity of a region of Southern California. The flexible estimation approach is introduced together with a diagnostic method for space-time point process, based on the interpretation of some second-order statistics, to analyze the dependence structure of observed data and suggest directions for fit improvement. In this paper we review a diagnostic method for space-time point processes based on the interpretation of the transformed version of some second-order statistics. The method is useful to analyze dependence structures of observed dat…

Kernel Spectral Angle Mapper

2016

This communication introduces a very simple generalization of the familiar spectral angle mapper (SAM) distance. SAM is perhaps the most widely used distance in chemometrics, hyperspectral imaging, and remote sensing applications. We show that a nonlinear version of SAM can be readily obtained by measuring the angle between pairs of vectors in a reproducing kernel Hilbert spaces. The kernel SAM generalizes the angle measure to higher-order statistics, it is a valid reproducing kernel, it is universal, and it has consistent geometrical properties that permit deriving a metric easily. We illustrate its performance in a target detection problem using very high resolution imagery. Excellent re…

On the First- and Second-Order Statistics of Selective Combining over Double Nakagami-m Fading Channels

2014

Ultimate Order Statistics-Based Prototype Reduction Schemes

2013

Published version of a chapter in the book: AI 2013: Advances in Artificial Intelligence. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-319-03680-9_42 The objective of Prototype Reduction Schemes (PRSs) and Border Identification (BI) algorithms is to reduce the number of training vectors, while simultaneously attempting to guarantee that the classifier built on the reduced design set performs as well, or nearly as well, as the classifier built on the original design set. In this paper, we shall push the limit on the field of PRSs to see if we can obtain a classification accuracy comparable to the optimal, by condensing the information in the data set into a single tr…