## 36 Citations

Needlet-Whittle Estimates on the Unit Sphere

- Mathematics
- 2012

We study the asymptotic behaviour of needlets-based approximate maximum likelihood estimators for the spectral parameters of Gaussian and isotropic spherical random fields. We prove consistency and…

Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields

- MathematicsStat. Methods Appl.
- 2016

The aim of this paper is to establish rates of convergence to Gaussianity for wavelet coefficients on circular Poisson random fields by using the Stein–Malliavin techniques and the concentration properties of so-called Mexican needlets on the circle.

Flexible-bandwidth Needlets

- Mathematics
- 2021

We investigate here a generalized construction of spherical wavelets/needlets which admits extra-flexibility in the harmonic domain, i.e., it allows the corresponding support in multipole (frequency)…

Consistency of a needlet spectral estimator on the sphere

- Mathematics
- 2008

The angular power spectrum of a stationary random field on the sphere is es- timated from the needlet coecients of a single realization, observed with increasingly fine resolution. The estimator we…

Spectral estimation on the sphere with needlets: high frequency asymptotics

- Mathematics
- 2011

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…

High-Frequency Tail Index Estimation by Nearly Tight Frames

- Mathematics
- 2013

This work develops the asymptotic properties (weak consistency and Gaussianity), in the high-frequency limit, of approximate maximum likelihood estimators for the spectral parameters of Gaussian and…

Normal Approximations for Wavelet Coefficients on Spherical Poisson Fields

- Mathematics, Physics
- 2012

Spin Needlets Spectral Estimation

- Mathematics, Physics
- 2009

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 in $S^2$ take as a value a curve (e.g. an…

## References

SHOWING 1-10 OF 17 REFERENCES

Asymptotics for spherical needlets

- Mathematics
- 2009

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…

Subsampling needlet coefficients on the sphere

- Mathematics
- 2009

In a recent paper, we analyzed the properties of a new kind of spherical wavelets (so-called needlets) for statistical inference procedures on spherical random fields; the results were mainly…

Spherical needlets for cosmic microwave background data analysis

- Mathematics
- 2008

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…

Spherical Needlets for CMB Data Analysis

- Mathematics
- 2007

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…

High frequency asymptotics for wavelet-based tests for Gaussianity and isotropy on the torus

- Mathematics
- 2006

The needlets bispectrum

- Physics
- 2008

The purpose of this paper is to join two different threads of the recent literature on random fields on the sphere, namely the statisti- cal analysis of higher order angular power spectra on one…

Localized Tight Frames on Spheres

- MathematicsSIAM J. Math. Anal.
- 2006

A new class of tight frames on the sphere is presented, based on pointwise localization of kernels arising in the spectral calculus for certain self-adjoint operators, and on a positive-weight quadrature formula for the sphere that the authors have recently developed.