Related papers: Optimal designs for three-dimensional shape analys…
In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the missorientation…
This short paper is concerned with the use of spherical t-designs as optimal designs for the spherical harmonic regression model in three dimensions over a range of specified criteria. The nature of the designs is explored and their…
Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…
Spherical regression, in which both covariates and responses lie on the sphere, arises in many scientific applications and has attracted considerable methodological attention in recent years. Despite this progress, constructing flexible and…
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…
Locally optimal designs for generalized linear models are derived at certain values of the regression parameters. In the present paper a general setup of the generalized linear model is considered. Analytic solutions for optimal designs are…
Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in…
We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The…
In 3D single particle imaging with X-ray free-electron lasers, particle orientation is not recorded during measurement but is instead recovered as a necessary step in the reconstruction of a 3D image from the diffraction data. Here we use…
In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is…
We consider a linear regression model with complex-valued response and predictors from a compact and connected Lie group. The regression model is formulated in terms of eigenfunctions of the Laplace-Beltrami operator on the Lie group. We…
In this paper optimal experimental designs for inverse quadratic regression models are determined. We consider two different parameterizations of the model and investigate local optimal designs with respect to the $c$-, $D$- and…
Algorithms which compute locally optimal continuous designs often rely on a finite design space or on repeatedly solving a complex non-linear program. Both methods require extensive evaluations of the Jacobian Df of the underlying model.…
This paper proposes a multi-shell sampling scheme and corresponding transforms for the accurate reconstruction of the diffusion signal in diffusion MRI by expansion in the spherical polar Fourier (SPF) basis. The sampling scheme uses an…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
The interference model has been widely used and studied in block experiments where the treatment for a particular plot has effects on its neighbor plots. In this paper, we study optimal circular designs for the proportional interference…
3D image processing constitutes nowadays a challenging topic in many scientific fields such as medicine, computational physics and informatics. Therefore, development of suitable tools that guaranty a best treatment is a necessity.…
In this paper we consider the problem of constructing $T$-optimal discriminating designs for Fourier regression models. We provide explicit solutions of the optimal design problem for discriminating between two Fourier regression models,…
This paper studies optimal designs for linear regression models with correlated effects for single responses. We introduce the concept of rhombic design to reduce the computational complexity and find a semi-algebraic description for the…
In this work we build optimal experimental designs for precise estimation of the functional coefficient of a function-on-function linear regression model where both the response and the factors are continuous functions of time. After…