Spin needlets spectral estimation
نویسندگان
چکیده
منابع مشابه
Spin Needlets Spectral Estimation
We consider the statistical analysis of random sections of a spin fibre bundle over the sphere. These may be thought of as random fields that at each point p ∈ S2 take as a value a curve (e.g. an ellipse) living in the tangent plane at that point TpS 2, rather than a number as in ordinary situations. The analysis of such fields is strongly motivated by applications, for instance polarization ex...
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Abstract: The angular power spectrum of a stationary random field on the sphere is estimated from the needlet coefficients of a single realization, observed with increasingly fine resolution. The estimator we consider is similar to the one recently used in practice by (Faÿ et al. 2008) to estimate the power spectrum of the Cosmic Microwave Background. The consistency of the estimator, in the as...
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Abstract: The purpose of this paper is to join two different threads of the recent literature on random fields on the sphere, namely the statistical analysis of higher order angular power spectra on one hand, and the construction of second-generation wavelets on the sphere on the other. To this aim, we introduce the needlets bispectrum and we derive a number of convergence results. Here, the li...
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We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This pro...
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Abstract We recall Mexican needlets from [5]. We derive an estimate for certain types of Legendre series, which we apply to the statistical properties of Mexican needlets. More precisely, we shall show that, under isotropy and Gaussianity assumptions, the Mexican needlet coefficients of a random field on the sphere are asymptotically uncorrelated, as the frequency parameter goes to infinity. Th...
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ژورنال
عنوان ژورنال: Electronic Journal of Statistics
سال: 2009
ISSN: 1935-7524
DOI: 10.1214/09-ejs448