Let q ≥ 1 be an integer, Sq be the unit sphere embedded in Rq+1, and μq be the volume element of Sq. For x0 ∈ Sq, and α ∈ (0, π), let Sα(x0) denote the cap {ξ ∈ Sq : x0 · ξ ≥ cosα}. We prove that for any integer m ≥ 1, there exists a positive constant c = c(q,m), independent of α, with the following property. Given an arbitrary set C of points in Sα(x0), satisftying the mesh norm condition max ...

In this paper we wish to present a new class of tight frames on the sphere. These frames have excellent pointwise localization and approximation properties. These properties are based on pointwise localization of kernels arising in the spectral calculus for certain self-adjoint operators, and on a positive-weight quadrature formula for the sphere that the authors have recently developed. Improv...

This paper studies properties of an estimator of mean-variance portfolio weights in a market model with multiple risky assets and a riskless asset. Theoretical formulas for the mean square error are derived in the case when asset excess returns are multivariate normally distributed and serially independent. The sensitivity of the portfolio estimator to errors arising from the estimation of the ...

In this paper, a recently developed numerical method to analyze dielectric-spectroscopy data is applied to α-phase polyvinylidene fluoride (PVDF). The numerical procedure is non-parametric and does not contain any of the extensively used empirical formulas mentioned in the literature. The method basically recovers the unknown distribution of relaxation times of the generalized dielectric functi...

This essay identifies the empirical facts about lobbying which are generally agreed upon in the literature. It then discusses challenges to empirical research in lobbying and provides examples of empirical methods that can be employed to overcome these challenges—with an emphasis on statistical measurement, identification, and casual inference. The essay then discusses the advantages, disadvant...