Search results for "Parametric"
showing 10 items of 980 documents
Tests and estimates of shape based on spatial signs and ranks
2009
Nonparametric procedures for testing and estimation of the shape matrix in the case of multivariate elliptic distribution are considered. Testing for sphericity is an important special case. The tests and estimates are based on the spatial sign and rank covariance matrices. The estimates based on the spatial sign covariance matrix and symmetrized spatial sign covariance matrix are Tyler's [A distribution-free M-estimator of multivariate scatter, Ann. Statist. 15 (1987), pp. 234–251] shape matrix and and Dümbgen's [On Tyler's M-functional of scatter in high dimension, Ann. Inst. Statist. Math. 50 (1998), pp. 471–491] shape matrix, respectively. The test based on the spatial sign covariance m…
Nonlinear parametric quantile models
2020
Quantile regression is widely used to estimate conditional quantiles of an outcome variable of interest given covariates. This method can estimate one quantile at a time without imposing any constraints on the quantile process other than the linear combination of covariates and parameters specified by the regression model. While this is a flexible modeling tool, it generally yields erratic estimates of conditional quantiles and regression coefficients. Recently, parametric models for the regression coefficients have been proposed that can help balance bias and sampling variability. So far, however, only models that are linear in the parameters and covariates have been explored. This paper …
Basing the Analysis of Comparative Bioavailability Trials on an Individualized Statistical Definition of Equivalence
1993
The conventional definition of bioequivalence in terms of population means only, is criticized for lacking relevance to the individual subject. Both approaches to bioequivalence assessment proposed here for avoiding this shortcoming, focus on the probability of an event induced by the response of a randomly selected subject to two formulations of a given active agent. The first approach leads to converting the basic idea underlying the well-known 75-rule into an exact statistical procedure. The second approach is of a parametric nature. It reduces bioequivalence assessment to testing against the alternative hypothesis that the standardized expected value of a Gaussian distribution is contai…
Multivariate Nonparametric Tests
2004
Multivariate nonparametric statistical tests of hypotheses are described for the one-sample location problem, the several-sample location problem and the problem of testing independence between pairs of vectors. These methods are based on affine-invariant spatial sign and spatial rank vectors. They provide affine-invariant multivariate generalizations of the univariate sign test, signed-rank test, Wilcoxon rank sum test, Kruskal–Wallis test, and the Kendall and Spearman correlation tests. While the emphasis is on tests of hypotheses, certain references to associated affine-equivariant estimators are included. Pitman asymptotic efficiencies demonstrate the excellent performance of these meth…
Efficient Estimation of Non-Linear Finite Population Parameters by Using Non-Parametrics
2013
Summary Currently, high precision estimation of non-linear parameters such as Gini indices, low income proportions or other measures of inequality is particularly crucial. We propose a general class of estimators for such parameters that take into account univariate auxiliary information assumed to be known for every unit in the population. Through a non-parametric model-assisted approach, we construct a unique system of survey weights that can be used to estimate any non-linear parameter that is associated with any study variable of the survey, using a plug-in principle. Based on a rigorous functional approach and a linearization principle, the asymptotic variance of the estimators propose…
A semiparametric approach to estimate reference curves for biophysical properties of the skin
2006
Reference curves which take one covariable into account such as the age, are often required in medicine, but simple systematic and efficient statistical methods for constructing them are lacking. Classical methods are based on parametric fitting (polynomial curves). In this chapter, we describe a new methodology for the estimation of reference curves for data sets, based on nonparametric estimation of conditional quantiles. The derived method should be applicable to all clinical or more generally biological variables that are measured on a continuous quantitative scale. To avoid the curse of dimensionality when the covariate is multidimensional, a new semiparametric approach is proposed. Th…
Optimization of the breeder zone cooling tubes of the DEMO Water-Cooled Lithium Lead breeding blanket
2016
Abstract The determination of an optimal configuration for the breeder zone (BZ) cooling tubes is one of the most important issues in the DEMO Water-Cooled Lithium Lead (WCLL) breeding blanket R&D activities, since BZ cooling tubes spatial distribution should ensure an efficient heat power removal from the breeder, avoiding hotspots occurrence in the thermal field. Within the framework of R&D activities supported by the HORIZON 2020 EUROfusion Consortium action on the DEMO WCLL breeding blanket design, a campaign of parametric analyses has been launched at the Department of Energy, Information Engineering and Mathematical Models of the University of Palermo (DEIM), in close cooperation with…
Solving fully randomized first-order linear control systems: Application to study the dynamics of a damped oscillator with parametric noise under sto…
2022
[EN] This paper is devoted to study random linear control systems where the initial condition, the final target, and the elements of matrices defining the coefficients are random variables, while the control is a stochastic process. The so-called Random Variable Transformation technique is adapted to obtain closed-form expressions of the probability density functions of the solution and of the control. The theoretical findings are applied to study the dynamics of a damped oscillator subject to parametric noise.
Ito and Stratonovich integrals for delta-correlated processes
1993
Abstract In this paper the generalization of the Itd and Stratonovich integrals for the case of non-linear systems excited by parametric delta-correlated processes is presented. This generalization gives a new light on the corrective coefficients in the stochastic differential equations driven by parametric delta-correlated processes. The full significance of these corrective terms is evidenced by means of some examples.
Stochastic integro-differential and differential equations of non-linear systems excited by parametric Poisson pulses
1997
Abstract The connection between stochastic integro-differential equation and stochastic differential equation of non-linear systems driven by parametric Poisson delta correlated processes is presented. It is shown that the two different formulations are fully equivalent in the case of external excitation. In the case of parametric type excitation the two formulation are equivalent if the non-linear argument in the integral representation is related by means of a series to the corresponding non-linear parametric term in the stochastic differential equation. Differential rules for the two representations to find moment equations of every order of the response are also compared.