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Reference points based transformation and approximation

Csaba Török (2013)

Kybernetika

Interpolating and approximating polynomials have been living separately more than two centuries. Our aim is to propose a general parametric regression model that incorporates both interpolation and approximation. The paper introduces first a new r -point transformation that yields a function with a simpler geometrical structure than the original function. It uses r ≥ 2 reference points and decreases the polynomial degree by r - 1 . Then a general representation of polynomials is proposed based on r ≥ 1 reference...

Rejection of nonharmonic disturbances in nonlinear systems

Shutang Liu, Yuan Jiang, Ping Liu (2010)

Kybernetika

This paper proposes an asymptotic rejection algorithm on the rejection of nonharmonic periodic disturbances for general nonlinear systems. The disturbances, which are produced by nonlinear exosystems, are nonharmonic and periodic. A new nonlinear internal model is proposed to deal with the disturbances. Further, a state feedback controller is designed to ensure that the system's state variables can asymptotically converge to zero, and the disturbances can be completely rejected. The proposed algorithm...

Reliability in the Rasch model

Patrícia Martinková, Karel Zvára (2007)

Kybernetika

This paper deals with the reliability of composite measurement consisting of true-false items obeying the Rasch model. A definition of reliability in the Rasch model is proposed and the connection to the classical definition of reliability is shown. As a modification of the classical estimator Cronbach's alpha, a new estimator logistic alpha is proposed. Finally, the properties of the new estimator are studied via simulations in the Rasch model.

Remarques sur le maximum de vraisemblance.

Catherine Huber, Mikhail Nikulin (1997)

Qüestiió

Some paradoxes on the maximum likelihood principle are presented and commented. We consider the properties of the maximum likelihood estimators as a particular case of the M-estimators. We propose a unified theory which includes non-dominated models. Several examples are given.

Reversible jump MCMC for two-state multivariate Poisson mixtures

Jani Lahtinen, Jouko Lampinen (2003)

Kybernetika

The problem of identifying the source from observations from a Poisson process can be encountered in fault diagnostics systems based on event counters. The identification of the inner state of the system must be made based on observations of counters which entail only information on the total sum of some events from a dual process which has made a transition from an intact to a broken state at some unknown time. Here we demonstrate the general identifiability of this problem in presence of multiple...

Risk bounds for new M-estimation problems

Nabil Rachdi, Jean-Claude Fort, Thierry Klein (2013)

ESAIM: Probability and Statistics

In this paper, we consider a new framework where two types of data are available: experimental data Y1,...,Yn supposed to be i.i.d from Y and outputs from a simulated reduced model. We develop a procedure for parameter estimation to characterize a feature of the phenomenon Y. We prove a risk bound qualifying the proposed procedure in terms of the number of experimental data n, reduced model complexity and computing budget m. The method we present is general enough to cover a wide range of applications....

Robust Bayesian estimation in a normal model with asymmetric loss function

Agata Boratyńska, Monika Drozdowicz (1999)

Applicationes Mathematicae

The problem of robust Bayesian estimation in a normal model with asymmetric loss function (LINEX) is considered. Some uncertainty about the prior is assumed by introducing two classes of priors. The most robust and conditional Γ-minimax estimators are constructed. The situations when those estimators coincide are presented.

Robust Bayesian estimation with asymmetric loss function

Agata Boratyńska (2002)

Applicationes Mathematicae

The problem of robust Bayesian estimation in some models with an asymmetric loss function (LINEX) is considered. Some uncertainty about the prior is assumed by introducing two classes of priors. The most robust and conditional Γ-minimax estimators are constructed. The situations when those estimators coincide are presented.

Robust estimation and forecasting for beta-mixed hierarchical models of grouped binary data.

Maxim A. Pashkevich, Yurij S. Kharin (2004)

SORT

The paper focuses on robust estimation and forecasting techniques for grouped binary data with misclassified responses. It is assumed that the data are described by the beta-mixed hierarchical model (the beta-binomial or the beta-logistic), while the misclassifications are caused by the stochastic additive distorsions of binary observations. For these models, the effect of ignoring the misclassifications is evaluated and expressions for the biases of the method-of-moments estimators and maximum...

Robust estimation based on spacings in weighted exponential models

Paweł Błażej, Jarosław Bartoszewicz (2007)

Applicationes Mathematicae

Using Zieliński's (1977, 1983) formalization of robustness Błażej (2007) obtained uniformly most bias-robust estimates (UMBREs) of the scale parameter for some statistical models (including the exponential model), in a class of linear functions of order statistics, when violations of the models are generated by weight functions. In this paper the UMBRE of the scale parameter, based on spacings, in two weighted exponential models is derived. Extensions of results of Bartoszewicz (1986, 1987) are...

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