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Confidence regions of minimal area for the scale-location parameter and their applications

A. Czarnowska, A. V. Nagaev (2001)

Applicationes Mathematicae

The area of a confidence region is suggested as a quality exponent of parameter estimation. It is shown that under very mild restrictions imposed on the underlying scale-location family there exists an optimal confidence region. Explicit formulae as well as numerical results concerning the normal, exponential and uniform families are presented. The question how to estimate the quantile function is also discussed.

Consistency of the least weighted squares under heteroscedasticity

Jan Ámos Víšek (2011)

Kybernetika

A robust version of the Ordinary Least Squares accommodating the idea of weighting the order statistics of the squared residuals (rather than directly the squares of residuals) is recalled and its properties are studied. The existence of solution of the corresponding extremal problem and the consistency under heteroscedasticity is proved.

Consistency of trigonometric and polynomial regression estimators

Waldemar Popiński (1998)

Applicationes Mathematicae

The problem of nonparametric regression function estimation is considered using the complete orthonormal system of trigonometric functions or Legendre polynomials e k , k=0,1,..., for the observation model y i = f ( x i ) + η i , i=1,...,n, where the η i are independent random variables with zero mean value and finite variance, and the observation points x i ∈ [ a , b ] , i=1,...,n, form a random sample from a distribution with density ϱ ∈ L 1 [ a , b ] . Sufficient and necessary conditions are obtained for consistency in the sense of the errors ∥ f - f ^ N ∥ , | f ( x ) - N ( x ) | , x ∈ [ a , b ] ,...

Constructing median-unbiased estimators in one-parameter families of distributions via stochastic ordering

Ryszard Zieliński (2003)

Applicationes Mathematicae

If θ ∈ Θ is an unknown real parameter of a given distribution, we are interested in constructing an exactly median-unbiased estimator θ̂ of θ, i.e. an estimator θ̂ such that a median Med(θ̂ ) of the estimator equals θ, uniformly over θ ∈ Θ. We shall consider the problem in the case of a fixed sample size n (nonasymptotic approach).

Contraste de modelos probabilísticos desde una perspectiva bayesiana.

José Miguel Bernardo (1982)

Trabajos de Estadística e Investigación Operativa

Se pone de manifiesto que el problema de contrastar si un conjunto de datos es o no compatible con un modelo probabilístico totalmente especificado puede ser reducido al problema de contrastar si una determinada transformación de los datos puede ser considerada como una muestra aleatoria de una distribución uniforme. Mediante la construcción de una nueva familia paramétrica de distribuciones, que contiene a la uniforme como caso particular, se propone un contraste bayesiano de uniformidad que constituye...

Contrastes de hipótesis basados en la (r,s)-divergencia: aplicación a distribuciones multinomiales y normales multivariantes.

Domingo Morales, Leandro Pardo, Miquel Salicrú, M.ª Luisa Menéndez (1992)

Qüestiió

En este trabajo se obtiene la distribución asintótica de la (r,s)-divergencia, introducida por Sharma y Mittal (1975), entre dos densidades fθ1 y fθ2, cuando θ2 es fijo y θ1 desconocido o bien cuando los dos son desconocidos. Se supone que los parámetros desconocidos se estiman de acuerdo con el principio de máxima verosimilitud. Como caso particular se obtienen las distribuciones asintóticas en el caso de poblaciones multinomiales. Se concluye el trabajo construyendo, sobre la base de los estadísticos...

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