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Change-point estimation from indirect observations. 1. Minimax complexity

A. Goldenshluger, A. Juditsky, A. B. Tsybakov, A. Zeevi (2008)

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

We consider the problem of nonparametric estimation of signal singularities from indirect and noisy observations. Here by singularity, we mean a discontinuity (change-point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide lower bounds for minimax risks and propose rate-optimal estimation procedures.

Change-Point problems: approaches and applications.

Adrian F. M. Smith (1980)

Trabajos de Estadística e Investigación Operativa

Problems of making inferences about abrupt changes in the mechanism underlying a sequence of observations are considered in both retrospective and on-line contexts. Among the topics considered are the Lindisfarne scribes problem; switching straight lines; manoeuvering targets, and shifts of level or slope in linear time series models. Summary analyses of data obtained in studies of schizophrenic and kidney transplant patients are presented.

Characterization of admissible linear estimators under extended balanced loss function

Buatikan Mirezi, Selahattin Kaçıranlar (2021)

Kybernetika

In this paper, we study the admissibility of linear estimator of regression coefficient in linear model under the extended balanced loss function (EBLF). The sufficient and necessary condition for linear estimators to be admissible are obtained respectively in homogeneous and non-homogeneous classes. Furthermore, we show that admissible linear estimator under the EBLF is a convex combination of the admissible linear estimator under the sum of square residuals and quadratic loss function.

Comparison of two methods for approximation of probability distributions with prescribed marginals

Albert Pérez, Milan Studený (2007)

Kybernetika

Let P be a discrete multidimensional probability distribution over a finite set of variables N which is only partially specified by the requirement that it has prescribed given marginals { P A ; A ∈ 𝒮 } , where 𝒮 is a class of subsets of N with ⋃ 𝒮 = N . The paper deals with the problem of approximating P on the basis of those given marginals. The divergence of an approximation P ^ from P is measured by the relative entropy H ( P | P ^ ) . Two methods for approximating P are compared. One of them uses formerly introduced concept of...

Compatibilidad del método de De Groot para llegar a un consenso con la fórmula de Bayes.

Enrique Caro, Juan Ignacio Domínguez, Francisco Javier Girón (1984)

Trabajos de Estadística e Investigación Operativa

En este artículo se prueba que el sencillo método propuesto por De Groot para llegar a un consenso cuando los varios decisores tienen opiniones diferentes expresadas en términos de distribuciones de probabilidad es compatible con la regla de Bayes cuando se tiene en cuenta la información muestral. Se demuestra que si se calculan primero las distribuciones a posteriori y después se aplica el método de De Groot para alcanzar un consenso (cuando esto sea posible), es lo mismo que realizar primero el...

Completitud esencial de la clase de controles basados en un proceso suficiente.

Pilar Ibarrola Muñoz, Javier Yáñez Gestoso (1985)

Trabajos de Estadística e Investigación Operativa

Se define en este artículo el concepto de proceso suficiente para un proceso de control, así como el de control basado en un proceso suficiente. Se demuestra a continuación que el conjunto de controles basados en un proceso suficiente forma una clase esencialmente completa; por consiguiente, dado un control, existe un control basado en el proceso suficiente que tiene el mismo coste esperado que el anterior.

Conceptual base of feature selection consulting system

Pavel Pudil, Jana Novovičová, Petr Somol, Radek Vrňata (1998)

Kybernetika

The paper briefly reviews recent advances in the methodology of feature selection (FS) and the conceptual base of a consulting system for solving FS problems. The reasons for designing a kind of expert or consulting system which would guide a less experienced user are outlined. The paper also attempts to provide a guideline which approach to choose with respect to the extent of a priori knowledge of the problem. The methods discussed here form the core of the software package being developed for...

Convexity inequalities for estimating generalized conditional entropies from below

Alexey E. Rastegin (2012)

Kybernetika

Generalized entropic functionals are in an active area of research. Hence lower and upper bounds on these functionals are of interest. Lower bounds for estimating Rényi conditional α -entropy and two kinds of non-extensive conditional α -entropy are obtained. These bounds are expressed in terms of error probability of the standard decision and extend the inequalities known for the regular conditional entropy. The presented inequalities are mainly based on the convexity of some functions. In a certain...

Criterio de maximización de la quietud esperada (invariante frente a traslaciones respecto a las utilidades).

María Angeles Gil Alvarez (1980)

Stochastica

In this paper we start from the following situation: a decision maker wants information about a certain parameter space for which he has a set of random variables with probability distribution depending on an unknown paremeter belonging to the mentioned space. Generally, we assume that the decision maker may observe values of any experiment but not of two simultaneous ones. This reason makes a comparison between them indispensable to choose the most appropriate for his objectives.Through the article...

Cross additivity - an application

Sandra Saraiva Ferreira, Dário Ferreira, João Tiago Mexia (2006)

Discussiones Mathematicae Probability and Statistics

We try to show that Discriminant Analysis can be considered as a branch of Statistical Decision Theory when viewed from a Bayesian approach. First we present the necessary measure theory results, next we briefly outline the foundations of Bayesian Inference before developing Discriminant Analysis as an application of Bayesian Estimation. Our approach renders Discriminant Analysis more flexible since it gives the possibility of classing an element as belonging to a group of populations. This possibility...

Decisión equivariante óptima en poblaciones con parámetro de localización y escala.

Ramón Ardanuy Albajar, M.ª del Mar Soldevilla Moreno (1981)

Trabajos de Estadística e Investigación Operativa

En este trabajo se trata el problema de decisión equivariante en poblaciones dependientes de un parámetro bidimensional del tipo de localización y escala, obteniendo la información a partir de un estadístico ordenado. Tras caracterizar las funciones de decisión equivariantes y encontrar la expresión para la función de decisión óptima, se ven condiciones, sobre la función de pérdida y distribución muestral, que sean suficientes para garantizar que la función de decisión equivariante óptima sea minimax...

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