Statistical modelling of deformation measurements.
Statistical models for deformable templates in image and shape analysis
High dimensional data are more and more frequent in many application fields. It becomes particularly important to be able to extract meaningful features from these data sets. Deformable template model is a popular way to achieve this. This paper is a review on the statistical aspects of this model as well as its generalizations. We describe the different mathematical frameworks to handle different data types as well as the deformations. We recall the theoretical convergence properties of the estimators...
Stochastic comparison of multivariate random sums
We establish preservation results for the stochastic comparison of multivariate random sums of stationary, not necessarily independent, sequences of nonnegative random variables. We consider convex-type orderings, i.e. convex, coordinatewise convex, upper orthant convex and directionally convex orderings. Our theorems generalize the well-known results for the stochastic ordering of random sums of independent random variables.
Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model
The aim of this paper is to establish a nonparametric estimate of some characteristics of the conditional distribution. Kernel type estimators for the conditional cumulative distribution function and for the successive derivatives of the conditional density of a scalar response variable Y given a Hilbertian random variable X are introduced when the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence...
Strongly consistent estimation in dependent errors-in-variables
Suitability of linearization of nonlinear problems not only in biology and medicine
Biology and medicine are not the only fields that present problems unsolvable through a linear models approach. One way to overcome this obstacle is to use nonlinear methods, even though these are not as thoroughly explored. Another possibility is to linearize and transform the originally nonlinear task to make it accessible to linear methods. In this aricle I investigate an easy and quick criterion to verify suitability of linearization of nonlinear problems via Taylor series expansion so that...
Test for Independence of the Variables with Missing Elements in One and the Same Column of the Empirical Correlation Matrix
2000 Mathematics Subject Classification: 62H15, 62H12.We consider variables with joint multivariate normal distribution and suppose that the sample correlation matrix has missing elements, located in one and the same column. Under these assumptions we derive the maximum likelihood ratio test for independence of the variables. We obtain also the maximum likelihood estimations for the missing values.
Testing hypotheses in universal models
A linear regression model, when a design matrix has not full column rank and a covariance matrix is singular, is considered. The problem of testing hypotheses on mean value parameters is studied. Conditions when a hypothesis can be tested or when need not be tested are given. Explicit forms of test statistics based on residual sums of squares are presented.
Tests estadísticos sobre la distribución exponencial basados en la distancia de Rao.
En este artículo se construyen varios tests sobre el parámetro de la distribución exponencial, basados en la distancia de Rao. Los tests así desarrollados son comparados con los tests básicos de la inferencia estadística.
Tests of independence of normal random variables with known and unknown variance ratio
In the paper, a new approach to construction test for independenceof two-dimensional normally distributed random vectors is given under the assumption that the ratio of the variances is known. This test is uniformly better than the t-Student test. A comparison of the power of these two tests is given. A behaviour of this test forsome ε-contamination of the original model is also shown. In the general case when the variance ratio is unknown, an adaptive test is presented. The equivalence between...
The Bayes estimator of the variance components and its admissibility
The linear model with variance-covariance components and jackknife estimation
Let be a biased estimate of the parameter based on all observations , , and let () be the same estimate of the parameter obtained after deletion of the -th observation. If the expectation of the estimators and are expressed as where is a known sequence of real numbers and is a function of , then this system of equations can be regarded as a linear model. The least squares method gives the generalized jackknife estimator. Using this method, it is possible to obtain the unbiased...
The locally best estimators of the first and second order parameters in epoch regression models
The multiple regression model where independent variables are measured unprecisely.
The Occurrence of Outliers in the Explanatory Variable Considered in an Errors-in-Variables Framework.
The use of copulas in the study of certain transforms of random variables with applications in finance.
Time-Reversion of VARMA processes by polynomical methods.
Two different however equivalent methods for derivation of estimators of parameters in deformation measurements
The aim of this paper is to develop two different methods for an executing of the deformation measurement and to prove that these two methods are equivalent which is a advantage for a conclusive verification of the results of the experiment in a practice.
Two stage linear model with constraints
Two-Stage Point Estimation with a Shrinkage Stopping Rule.