Optimal designs for regression with spherical data

10/28/2017
by   Holger Dette, et al.
0

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 distribution or the grain boundary distribution (depending on a four dimensional spherical predictor) are represented by series of hyperspherical harmonics, which are estimated from experimental or simulated data. For this type of estimation problems we explicitly determine optimal designs with respect to Kiefers Φ_p-criteria and a class of orthogonally invariant information criteria recently introduced in the literature. In particular, we show that the uniform distribution on the m-dimensional sphere is optimal and construct discrete and implementable designs with the same information matrices as the continuous optimal designs. Finally, we illustrate the advantages of the new designs for series estimation by hyperspherical harmonics, which are symmetric with respect to the first and second crystallographic point group.

READ FULL TEXT
research
07/31/2019

Optimization-based quasi-uniform spherical t-design and generalized multitaper for complex physiological time series

Motivated by the demand to analyze complex physiological time series, we...
research
11/17/2020

A variational characterisation of projective spherical designs over the quaternions

We give an inequality on the packing of vectors/lines in quaternionic Hi...
research
03/08/2023

Sketching with Spherical Designs for Noisy Data Fitting on Spheres

This paper proposes a sketching strategy based on spherical designs, whi...
research
09/14/2020

Designing experiments for estimating an appropriate outlet size for a silo type problem

The problem of jam formation during the discharge by gravity of granular...
research
01/09/2023

Optimal Subsampling Design for Polynomial Regression in one Covariate

Improvements in technology lead to increasing availability of large data...
research
07/29/2020

Equivalence theorems for compound design problems with application in mixed models

In the present paper we consider design criteria which depend on several...
research
01/16/2023

Universal minima of potentials of certain spherical designs contained in the fewest parallel hyperplanes

We find the set of all universal minimum points of the potential of the ...

Please sign up or login with your details

Forgot password? Click here to reset