Related papers: Optimal Designs for Spherical Harmonic Regression
In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control.…
We consider optimal designs for the Kiefer cirteria, which include the E-criterion as a particular case, and the G-criterion in random coefficients regression (RCR) models. We obtain general the Kiefer criteria for approximate designs and…
We investigate imaging by spherically symmetric absolute instruments that provide perfect imaging in the sense of geometrical optics. We derive a number of properties of such devices, present a general method for designing them and use this…
We derive new relationships expressing solid spherical harmonics as series of toroidal harmonics and vice versa. The expansions include regular and irregular spherical harmonics, ring and axial toroidal harmonics of even and odd parity…
The problem of constructing optimal discriminating designs for a class of regression models is considered. We investigate a version of the $T_p$-optimality criterion as introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 289-303]. The…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…
A common goal in the study of high dimensional and complex system is to model the system by a low order representation. In this letter we propose a general approach for assessing the quality of a reduced order model for high dimensional…
We consider the problem of computing optimal experimental design on a finite design space with respect to a compound Bayes risk criterion, which includes the linear criterion for prediction in a random coefficient regression model. We show…
Minimax designs provide a uniform coverage of a design space $\mathcal{X} \subseteq \mathbb{R}^p$ by minimizing the maximum distance from any point in this space to its nearest design point. Although minimax designs have many useful…
We improve the existing results of optimal partial profile paired choice designs and provide new designs for situations where the choice set sizes are greater than two. The optimal designs are obtained under the main effects models and the…
Two-dimensional, resonant scanners have been utilized in a large variety of imaging modules due to their compact form, low power consumption, large angular range, and high speed. However, resonant scanners have problems with non-optimal and…
Spherical coverings on the S2 sphere and their algebraic numbers are given for the putatively optimal global solutions for some n-congruent spherical caps with minimal radius to completely cover the S2 sphere. A few locally optimal…
Modeling real processes often results in several suitable models. In order to be able to distinguish, or discriminate, which model best represents a phenomenon, one is interested, e.g., in so-called T-optimal designs. These consist of the…
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…
This paper deals exclusively with crossover designs for the purpose of comparing t test treatments with a control treatment when the number of periods is no larger than t+1. Among other results it specifies sufficient conditions for a…
Spectroscopic redshift surveys offer great prospects for constraining the dark sector in cosmology. Future surveys will however be both deep and wide and will thus require an analysis in 3-dimensional spherical geometry. We review and…
This paper studies the problem of identifying directions of axial symmetry in multivariate distributions. Theoretical results are derived on how the measure or cardinality of the set of symmetry directions relates to spherical symmetry. The…
In psychological research often paired comparisons are used in which either full or partial profiles of the alternatives described by a common set of two-level attributes are presented. For this situation the problem of finding optimal…
We establish several fundamental properties of analysis-suitable T-splines which are important for design and analysis. First, we characterize T-spline spaces and prove that the space of smooth bicubic polynomials, defined over the extended…