arXiv subjects

Andrej Pázman

Publications and source records attributed to Andrej Pázman.

4 recordsLinked to original sources

arXiv2025

Practical aspects of the virtual noise convex optimum design approach for correlated responses

In this paper we present several practically-oriented extensions and considerations for the virtual noise method in optimal design under correlation. First we introduce a slightly modified virtual noise representation which further illuminates the parallels to the classical design approach for uncorrelated observations. We suggest more efficient algorithms to obtain the design measures. Furthermore, we show that various convex relaxation methods used for sensor selection are special cases of our approach and can be solved within our framework. Finally, we provide practical guidelines on how to generally approach a design problem with correlated observations and demonstrate how to utilize the virtual noise method in this context in a meaningful way.

stat.ME↗

arXiv2021

A convex approach to optimum design of experiments with correlated observations

Optimal design of experiments for correlated processes is an increasingly relevant and active research topic. Present methods have restricted possibilities to judge their quality. To fill this gap, we complement the virtual noise approach by a convex formulation leading to an equivalence theorem comparable to the uncorrelated case and to an algorithm giving an upper performance bound against which alternative design methods can be judged. Moreover, a method for generating exact designs follows naturally. We exclusively consider estimation problems on a finite design space with a fixed number of elements. A comparison on some classical examples from the literature as well as a real application is provided.

math.ST↗

arXiv2015

Optimum design via I-divergence for stable estimation in generalized regression models

Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the asymptotic properties of maximal likelihood (ML) estimators in such models. However, in finite sample experiments there could be problems with identifiability, stability and uniqueness of the ML estimate, which are not reflected by the information matrices. In Pázman and Pronzato (2014) is discussed how to solve some of these estimability issues on the design stage of an experiment in standard nonlinear regression. Here we want to extend this design methodology to more general models based on exponential families of distributions (binomial, Poisson, normal with parametrized variances, etc.). The main tool for that is the information (or Kullback-Leibler) divergence, which is closely related to the ML estimation.

math.ST↗

arXiv2014

Optimum design accounting for the global nonlinear behavior of the model

Among the major difficulties that one may encounter when estimating parameters in a nonlinear regression model are the nonuniqueness of the estimator, its instability with respect to small perturbations of the observations and the presence of local optimizers of the estimation criterion. We show that these estimability issues can be taken into account at the design stage, through the definition of suitable design criteria. Extensions of $E$-, $c$- and $G$-optimality criteria are considered, which when evaluated at a given $θ^0$ (local optimal design), account for the behavior of the model response $η(θ)$ for $θ$ far from $θ^0$. In particular, they ensure some protection against close-to-overlapping situations where $\|η(θ)-η(θ^0)\|$ is small for some $θ$ far from $θ^0$. These extended criteria are concave and necessary and sufficient conditions for optimality (equivalence theorems) can be formulated. They are not differentiable, but when the design space is finite and the set $Θ$ of admissible $θ$ is discretized, optimal design forms a linear programming problem which can be solved directly or via relaxation when $Θ$ is just compact. Several examples are presented.

math.ST↗