A generalized beta function and associated probability density.
A generalized bivariate lifetime distribution based on parallel-series structures
In this paper, a generalized bivariate lifetime distribution is introduced. This new model is constructed based on a dependent model consisting of two parallel-series systems which have a random number of parallel subsystems with fixed components connected in series. The probability that one system fails before the other one is measured by using competing risks. Using the extreme-value copulas, the dependence structure of the proposed model is studied. Kendall's tau, Spearman's rho and tail dependences...
A generalized Markov decision process
A Generalized Maximum Likelihood Characterization of the Normal Distribution.
A Generalized Model of PAC Learning and its Applicability
We combine a new data model, where the random classification is subjected to rather weak restrictions which in turn are based on the Mammen−Tsybakov [E. Mammen and A.B. Tsybakov, Ann. Statis. 27 (1999) 1808–1829; A.B. Tsybakov, Ann. Statis. 32 (2004) 135–166.] small margin conditions, and the statistical query (SQ) model due to Kearns [M.J. Kearns, J. ACM 45 (1998) 983–1006] to what we refer to as PAC + SQ model. We generalize the class conditional constant noise (CCCN) model introduced by Decatur...
A generalized residual information measure and its properties.
A Geometric Appraoch to Finite Sample and Large Deviation Properties in Two-Way ANOVA with Spherically Distributed Error Vectors.
A geometric approach to correlation inequalities in the plane
By elementary geometric arguments, correlation inequalities for radially symmetric probability measures are proved in the plane. Precisely, it is shown that the correlation ratio for pairs of width-decreasing sets is minimized within the class of infinite strips. Since open convex sets which are symmetric with respect to the origin turn out to be width-decreasing sets, Pitt’s Gaussian correlation inequality (the two-dimensional case of the long-standing Gaussian correlation conjecture) is derived...
A geometric approach to measuring dependence between random vectors
A geometry on the space of probabilities (II). Projective spaces and exponential families.
In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...
A Global Approach to the Comparison of Clustering Results
The discovery of knowledge in the case of Hierarchical Cluster Analysis (HCA) depends on many factors, such as the clustering algorithms applied and the strategies developed in the initial stage of Cluster Analysis. We present a global approach for evaluating the quality of clustering results and making a comparison among different clustering algorithms using the relevant information available (e.g. the stability, isolation and homogeneity of the clusters). In addition, we present a visual method...
A Gram-Schmidt orthogonalizing process of design matrices in linear models as an estimating procedure of covariance components.
Se considera un modelo lineal mixto multivariante equilibrado sin interacción para el que las matrices de las formas cuadráticas necesarias para estimar la covarianza de las componentes se expresan mediante operadores lineales en espacios con producto interior de dimensión finita. El propósito de este artículo es demostrar que las formas cuadráticas obtenidas por el proceso de ortogonalización de Gram-Schmidt de las matrices de diseño son combinaciones lineales de las formas cuadráticas derivadas...
A graph-based estimator of the number of clusters
Assessing the number of clusters of a statistical population is one of the essential issues of unsupervised learning. Given n independent observations X1,...,Xn drawn from an unknown multivariate probability density f, we propose a new approach to estimate the number of connected components, or clusters, of the t-level set . The basic idea is to form a rough skeleton of the set using any preliminary estimator of f, and to count the number of connected components of the resulting graph. Under...
A haplotype block model for fine mapping of quantitative trait loci regulating HIV-1 pathogenesis.
A homogeneity test of large dimensional covariance matrices under non-normality
A test statistic for homogeneity of two or more covariance matrices is presented when the distributions may be non-normal and the dimension may exceed the sample size. Using the Frobenius norm of the difference of null and alternative hypotheses, the statistic is constructed as a linear combination of consistent, location-invariant, estimators of trace functions that constitute the norm. These estimators are defined as -statistics and the corresponding theory is exploited to derive the normal limit...
A Journey from Statistics and Probability to Risk Theory An interview with Ludger Rüschendorf
A Kantorovich-type Convergence Analysis for the Gauss-Newton-Method.
A large sample study of nonparametric proportional hazard regression model
A learning algorithm combining functional discriminant coordinates and functional principal components
A new type of discriminant space for functional data is presented, combining the advantages of a functional discriminant coordinate space and a functional principal component space. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on 35 functional data sets (time series). Experiments show that constructed combined space provides a higher quality of classification of LDA method compared with component spaces.
A Less Sensitive Linear Detector for the Change Point Based on Kernel Smoothing Method.