On weak convergence of sequences of measures
One multivariate linear model with nuisance parameters
One of the calibration problems
One singular multivariate linear model with nuisance parameters
The multivariate linear model, in which the matrix of the first order parameters is divided into two matrices: to the matrix of the useful parameters and to the matrix of the nuisance parameters, is considered.
Optimal nonlinear transformations of random variables
In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions....
Optimal quantization for the one–dimensional uniform distribution with Rényi--entropy constraints
We establish the optimal quantization problem for probabilities under constrained Rényi--entropy of the quantizers. We determine the optimal quantizers and the optimal quantization error of one-dimensional uniform distributions including the known special cases (restricted codebook size) and (restricted Shannon entropy).
Optimal solutions of multivariate coupling problems
Some necessary and some sufficient conditions are established for the explicit construction and characterization of optimal solutions of multivariate transportation (coupling) problems. The proofs are based on ideas from duality theory and nonconvex optimization theory. Applications are given to multivariate optimal coupling problems w.r.t. minimal -type metrics, where fairly explicit and complete characterizations of optimal transportation plans (couplings) are obtained. The results are of interest...
Optimal subspaces and constrained principal component analysis.
Optimization of the size of nonsensitiveness regions
The problem is to determine the optimum size of nonsensitiveness regions for the level of statistical tests. This is closely connected with the problem of the distribution of quadratic forms.
Orbital semilinear copulas
We introduce four families of semilinear copulas (i.e. copulas that are linear in at least one coordinate of any point of the unit square) of which the diagonal and opposite diagonal sections are given functions. For each of these families, we provide necessary and sufficient conditions under which given diagonal and opposite diagonal functions can be the diagonal and opposite diagonal sections of a semilinear copula belonging to that family. We focus particular attention on the family of orbital...
Original title unknown
Outliers in models with constraints
Outliers in univariate and multivariate regression models with constraints are under consideration. The covariance matrix is assumed either to be known or to be known only partially.
Overview of Recent Results in Growth-curve-type Multivariate Linear Models
The Extended Growth Curve Model (ECGM) is a multivariate linear model connecting different multivariate regression models in sample subgroups through common variance matrix. It has the form: Here, matrices contain subgroup division indicators, and corresponding regressors. If , we speak about (ordinary) Growth Curve Model. The model has already its age (it dates back to 1964), but it has many important applications. That is why it is still intensively studied. Many articles investigating...
Paradigme logique des écritures relationnelles de quelques critères fondamentaux d'association
Parameterization and R-peak error estimations of ECG signals using independent component analysis.
Parametric and nonparametric empirical regression models: case study of copper bromide laser generation.
Paramétrisation et analyse des correspondances
PC-PARIS - An Interactive Software System for Statistical Pattern Recognition
Perturbation des poids des unités statistiques et approximation en analyse en composantes principales
Pirámides indexadas y disimilaridades piramidales.
En este trabajo se pretende una formalización de las bases matemáticas sobre las que se amparan los modelos de clasificación y representación piramidal, estableciéndose para ello una relación entre los conceptos de pirámide indexada y disimilaridad piramidal. Asimismo se precisa el concepto de información redundante, contenida en una estructura piramidal, y se dan criterios objetivos para poder prescindir de ella sin que ello suponga una modificación de la estructura piramidal.