Power properties if invariant tests for spatial autocorrelation in linear regression

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is include

Subwavelength focusing of light without evanescent waves by an array of nanoholes

We provide the first evidence of free-space subwavelength focusing without evanescent fields using a photonic nano-structure. Hot-spots smaller than half of the wavelength were observed at distances of tens of wavelengths from the structure

Nanoscale tuneable light source

We report on a new type of optical source, a 'light-well', which can be used as a nanoscale tuneable emitter. Optical and plasmonic radiation is generated as an electron beam passes through a channel in a periodically layered metal-dielectric nanostructure. With a lateral size of just a few hundred nanometers, and an emission intensity of ~200 W/cm2 such light-wells may be employed in nanophotonic circuits as chip-scale free-electron light sources, or in densely packed ensembles for optical memory and display applications