A new method for identifying outlying subsets of data
A non asymptotic penalized criterion for gaussian mixture model selection
Specific Gaussian mixtures are considered to solve simultaneously variable selection and clustering problems. A non asymptotic penalized criterion is proposed to choose the number of mixture components and the relevant variable subset. Because of the non linearity of the associated Kullback-Leibler contrast on Gaussian mixtures, a general model selection theorem for maximum likelihood estimation proposed by [Massart Concentration inequalities and model selection Springer, Berlin (2007). Lectures...
A non asymptotic penalized criterion for Gaussian mixture model selection
Specific Gaussian mixtures are considered to solve simultaneously variable selection and clustering problems. A non asymptotic penalized criterion is proposed to choose the number of mixture components and the relevant variable subset. Because of the non linearity of the associated Kullback-Leibler contrast on Gaussian mixtures, a general model selection theorem for maximum likelihood estimation proposed by [Massart Concentration inequalities and model selection Springer, Berlin (2007). Lectures...
A non-iterative alternative to ordinal log-linear models.
A nonparametric test of zero intrapair correlation
The author applies the test criterion of P. Rothety to the statistical analysis of the positive correclation of symmetric pairs of observations. In this particular case he arrives at some new results. His work ends with a general proof of the consistency of Rothery's test.
A note on Anderson's note on a stationary autoregressive process
A form of the covariance matrix of a weakly stationary first-order autoregressive process is established.
A note on biconic copulas
We describe a class of bivariate copulas having a fixed diagonal section. The obtained class contains both the Fréchet upper and lower bounds and it allows to describe non-trivial tail dependence coefficients along both the diagonals of the unit square.
A Note on Generalized Wald's Method.
A note on order statistics from symmetrically distributed samples
We present a first moment distribution-free bound on expected values of L-statistics as well as properties of some numerical characteristics of order statistics, in the case when the observations are possibly dependent symmetrically distributed about the common mean. An actuarial interpretation of the presented bound is indicated.
A Note on Some Wishart Expectations.
A note on stability of multivariate distributions.
In this note we give an elementary proof of a characterization for stability of multivariate distributions by considering a functional equation.
A Note on the Characterization of the Multivariate Normal Distribution.
A note on the computational complexity of hierarchical overlapping clustering
In this paper the computational complexity of the problem of the approximation of a given dissimilarity measure on a finite set by a -ultrametric on and by a Robinson dissimilarity measure on is investigared. It is shown that the underlying decision problems are NP-complete.
A note on the continuity of projection matrices with application to the asymptotic distribution of quadratic forms
This paper investigates the continuity of projection matrices and illustrates an important application of this property to the derivation of the asymptotic distribution of quadratic forms. We give a new proof and an extension of a result of Stewart (1977).
A note on the Galambos copula and its associated Bernstein function
There is an infinite exchangeable sequence of random variables {Xk}k∈ℕ such that each finitedimensional distribution follows a min-stable multivariate exponential law with Galambos survival copula, named after [7]. A recent result of [15] implies the existence of a unique Bernstein function Ψ associated with {Xk}k∈ℕ via the relation Ψ(d) = exponential rate of the minimum of d members of {Xk}k∈ℕ. The present note provides the Lévy–Khinchin representation for this Bernstein function and explores some...
A note on the IPF algorithm when the marginal problem is unsolvable
In this paper we analyze the asymptotic behavior of the IPF algorithm for the problem of finding a 2x2x2 contingency table whose pair marginals are all equal to a specified 2x2 table, depending on a parameter. When this parameter lies below a certain threshold the marginal problem has no solution. We show that in this case the IPF has a “period three limit cycle” attracting all positive initial tables, and a bifurcation occur when the parameter crosses the threshold.
A note on the matrix Haffian.
This note contains a transparent presentation of the matrix Haffian. A basic theorem links this matrix and the differential ofthe matrix function under investigation, viz ∇F(X) and dF(X).Frequent use is being made of matrix derivatives as developed by Magnus and Neudecker.
A Note on the Multiple Indicator-Multiple Cause Model with Sevweral Latent Variables
A note on the strong consistency of least squares estimates
The strong consistency of least squares estimates in multiples regression models with i.i.d. errors is obtained under assumptions on the design matrix and moment restrictions on the errors.
A novel robust principal component analysis method for image and video processing
The research on the robust principal component analysis has been attracting much attention recently. Generally, the model assumes sparse noise and characterizes the error term by the -norm. However, the sparse noise has clustering effect in practice so using a certain -norm simply is not appropriate for modeling. In this paper, we propose a novel method based on sparse Bayesian learning principles and Markov random fields. The method is proved to be very effective for low-rank matrix recovery...