In this correspondence we derive the asymptotic distribution of the MUSIC null spectrum, from which an exact expression of the asymptotic variance of the MUSIC null spectrum can be obtained. The result presented in this correspondence is a simpler alternative and a special case of a more general result recently obtained by Lee and Wengrovitz.

Hyperuniform point patterns are characterized by vanishing infinitewavelength density fluctuations and encompass all crystal structures, certain quasiperiodic systems, and special disordered point patterns (Torquato and Stillinger 2003 Phys. Rev. E 68 041113). This paper generalizes the notion of hyperuniformity to include also two-phase random heterogeneous media. Hyperuniform random media do ...

We consider the problem of estimating the proportion θ of true null hypotheses in a multiple testing context. The setup is classically modeled through a semiparametric mixture with two components: a uniform distribution on interval [0, 1] with prior probability θ and a nonparametric density f . We discuss asymptotic efficiency results and establish that two different cases occur whether f vanis...

A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged. The nearby points are chosen to maximize the variance reduction. We study in detail the case of univariate local linear regression. While ...

We use the model-calibrated pseudo empirical likelihood method to construct estimators for the finite population distribution function. Under an assumed superpopulation working model, the proposed estimators have minimum model expectation of asymptotic design-based variance among a class of estimators and therefore are optimal in that class. The estimators are asymptotically designunbiased irre...

Consider the standard Gaussian nonparametric regression problem. The observations are (xi, yi) where and where ~i are iid with finite fourth moment p4 < oo. This article presents a class of difference-based kernel estimators for the variance *AMS 2000 Subject Classification 62G08, 62G20 t ~ e ~ w o r d s and Phrases: Nonparametric regression, Variance estimation, Asymptotic minimaxity he work o...

Precise estimation of expected Darwinian fitness is a central component of life history analysis. Our methods provide precise estimation by incorporating general envelope methodology into the aster modeling framework. This level of precision provided from out methods allow researchers to draw stronger conclusions about the driving forces of Darwinian fitness from their life history analyses tha...