Asymptotic Uncorrelation for Mexican Needlets

2008/06/18 by Azita Mayeli, Mayeli, Azita · 1 citation
Computer Science · Engineering · Mathematics · #33C55 #62M40 #65T60 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Statistics Theory (math.ST) #math.FA #math.ST #msc:33C55 #msc:62M40 #msc:65T60 #stat.TH

paper · pdf · doi:10.48550/arxiv.0806.3009

13 pages

openalex publication_date 2008/06/18 · arxiv created 2009/04/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. This property is important in the analysis of cosmic microwave background radiation.

Citations

• Nearly Tight Frames and Space-Frequency Analysis on Compact Manifolds

Cited by

• Consistency of a needlet spectral estimator on the sphere

Related

• Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields
• Tail Behaviour of Mexican Needlets
• Consistency of a needlet spectral estimator on the sphere
• Asymptotic Behaviour of Level Sets of Needlet Random Fields
• High-Frequency Tail Index Estimation by Nearly Tight Frames