In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological data. In the p
resent work, we exploit the asymptotic uncorrelation of random needlet coefficients at fixed angular distances to construct subsampling statistics evaluated on Voronoi cells on the sphere. We illustrate how such statistics can be used for isotropy tests and for bootstrap estimation of nuisance parameters, even when a single realization of the spherical random field is observed. The asymptotic theory is developed in detail in the high resolution sense.
This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called {it needlets}. We establish a minimax result and prove its optimality. We are
motivated by astrophysical applications, in particular in connection with the analysis of ultra high energy cosmic rays.
We discuss Spherical Needlets and their properties. Needlets are a form of spherical wavelets which do not rely on any kind of tangent plane approximation and enjoy good localization properties in both pixel and harmonic space; moreover needlets coef
ficients are asymptotically uncorrelated at any fixed angular distance, which makes their use in statistical procedures very promising. In view of these properties, we believe needlets may turn out to be especially useful in the analysis of Cosmic Microwave Background (CMB) data on the incomplete sky, as well as of other cosmological observations. As a final advantage, we stress that the implementation of needlets is computationally very convenient and may rely completely on standard data analysis packages such as HEALPix.
