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Model selection for regression on a random design

Yannick Baraud (2010)

ESAIM: Probability and Statistics

We consider the problem of estimating an unknown regression function when the design is random with values in ℝ k . Our estimation procedure is based on model selection and does not rely on any prior information on the target function. We start with a collection of linear functional spaces and build, on a data selected space among this collection, the least-squares estimator. We study the performance of an estimator which is obtained by modifying this least-squares estimator on a set of small...

Modelización de datos longitudinales con estructuras de covarianza no estacionarias: modelos de coeficientes aleatorios frente a modelos alternativos.

Vicente Núñez-Antón, Dale L. Zimmerman (2001)

Qüestiió

Un tema que ha suscitado el interés de los investigadores en datos longitudinales durante las dos últimas décadas, ha sido el desarrollo y uso de modelos paramétricos explícitos para la estructura de covarianza de los datos. Sin embargo, el análisis de estructuras de covarianza no estacionarias en el contexto de datos longitudinales no se ha realizado de forma detallada principalmente debido a que las distintas aplicaciones no hacían necesario su uso. Muchos son los modelos propuestos recientemente,...

Modified minimax quadratic estimation of variance components

Viktor Witkovský (1998)

Kybernetika

The paper deals with modified minimax quadratic estimation of variance and covariance components under full ellipsoidal restrictions. Based on the, so called, linear approach to estimation variance components, i. e. considering useful local transformation of the original model, we can directly adopt the results from the linear theory. Under normality assumption we can can derive the explicit form of the estimator which is formally find to be the Kuks–Olman type estimator.

Multistage regression model

Lubomír Kubáček (1986)

Aplikace matematiky

Necessary and sufficient conditions are given under which the best linear unbiased estimator (BLUE) β ^ i ( Y 1 , ⋯ , Y i ) is identical with the BLUE β ^ i ( β ^ 1 , ⋯ , β ^ i - 1 , Y i ) ; Y 1 ⋯ , Y i are subvectors of the random vector Y in a general regression model ( Y , X β , ∑ ) , ( β 1 ' , ⋯ , β i ' ) ' = β a vector of unknown parameters; the design matrix X having a special so called multistage struture and the covariance matrix ∑ are given.

Multivariate models with constraints confidence regions

Lubomír Kubáček (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In multivariate linear statistical models with normally distributed observation matrix a structure of a covariance matrix plays an important role when confidence regions must be determined. In the paper it is assumed that the covariance matrix is a linear combination of known symmetric and positive semidefinite matrices and unknown parameters (variance components) which are unbiasedly estimable. Then insensitivity regions are found for them which enables us to decide whether plug-in approach can...

Multivariate statistical models; solvability of basic problems

Lubomír Kubáček (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Multivariate models frequently used in many branches of science have relatively large number of different structures. Sometimes the regularity condition which enable us to solve statistical problems are not satisfied and it is reasonable to recognize it in advance. In the paper the model without constraints on parameters is analyzed only, since the greatness of the class of such problems in general is out of the size of the paper.

New M-estimators in semi-parametric regression with errors in variables

Cristina Butucea, Marie-Luce Taupin (2008)

Annales de l'I.H.P. Probabilités et statistiques

In the regression model with errors in variables, we observe n i.i.d. copies of (Y, Z) satisfying Y=fθ0(X)+ξ and Z=X+ɛ involving independent and unobserved random variables X, ξ, ɛ plus a regression function fθ0, known up to a finite dimensional θ0. The common densities of the Xi’s and of the ξi’s are unknown, whereas the distribution of ɛ is completely known. We aim at estimating the parameter θ0 by using the observations (Y1, Z1), …, (Yn, Zn). We propose an estimation procedure based on the least...

Non-central generalized F distributions

Célia Nunes, João Tiago Mexia (2006)

Discussiones Mathematicae Probability and Statistics

The quotient of two linear combinations of independent chi-squares will have a generalized F distribution. Exact expressions for these distributions when the chi-square are central and those in the numerator or in the denominator have even degrees of freedom were given in Fonseca et al. (2002). These expressions are now extended for non-central chi-squares. The case of random non-centrality parameters is also considered.

Currently displaying 341 – 360 of 657