6 research outputs found
Adaptive Nonparametric Regression on Spin Fiber Bundles
The construction of adaptive nonparametric procedures by means of wavelet
thresholding techniques is now a classical topic in modern mathematical
statistics. In this paper, we extend this framework to the analysis of
nonparametric regression on sections of spin fiber bundles defined on the
sphere. This can be viewed as a regression problem where the function to be
estimated takes as its values algebraic curves (for instance, ellipses) rather
than scalars, as usual. The problem is motivated by many important
astrophysical applications, concerning for instance the analysis of the weak
gravitational lensing effect, i.e. the distortion effect of gravity on the
images of distant galaxies. We propose a thresholding procedure based upon the
(mixed) spin needlets construction recently advocated by Geller and Marinucci
(2008,2010) and Geller et al. (2008,2009), and we investigate their rates of
convergence and their adaptive properties over spin Besov balls.Comment: 40 page
Adaptive Density Estimation on the Circle by Nearly-Tight Frames
This work is concerned with the study of asymptotic properties of
nonparametric density estimates in the framework of circular data. The
estimation procedure here applied is based on wavelet thresholding methods: the
wavelets used are the so-called Mexican needlets, which describe a nearly-tight
frame on the circle. We study the asymptotic behaviour of the -risk
function for these estimates, in particular its adaptivity, proving that its
rate of convergence is nearly optimal.Comment: 30 pages, 3 figure
Adaptive estimation in the nonparametric random coefficients binary choice model by needlet thresholding
In the random coefficients binary choice model, a binary variable equals 1
iff an index is positive.The vectors and are
independent and belong to the sphere in .We
prove lower bounds on the minimax risk for estimation of the density
over Besov bodies where the loss is a power of the
norm for . We show that a hard
thresholding estimator based on a needlet expansion with data-driven thresholds
achieves these lower bounds up to logarithmic factors
Adaptive nonparametric regression on spin fiber bundles
AbstractThe construction of adaptive nonparametric procedures by means of wavelet thresholding techniques is now a classical topic in modern mathematical statistics. In this paper, we extend this framework to the analysis of nonparametric regression on sections of spin fiber bundles defined on the sphere. This can be viewed as a regression problem where the function to be estimated takes as its values algebraic curves (for instance, ellipses) rather than scalars, as usual. The problem is motivated by many important astrophysical applications, concerning, for instance, the analysis of the weak gravitational lensing effect, i.e. the distortion effect of gravity on the images of distant galaxies. We propose a thresholding procedure based upon the (mixed) spin needlets construction recently advocated by Geller and Marinucci (2008, 2010) and Geller et al. (2008, 2009), and we investigate their rates of convergence and their adaptive properties over spin Besov balls
Adaptive nonparametric regression on spin fiber bundles
The construction of adaptive nonparametric procedures by means of wavelet thresholding techniques is now a classical topic in modern mathematical statistics. In this paper, we extend this framework to the analysis of nonparametric regression on sections of spin fiber bundles defined on the sphere. This can be viewed as a regression problem where the function to be estimated takes as its values algebraic curves (for instance, ellipses) rather than scalars, as usual. The problem is motivated by many important astrophysical applications, concerning, for instance, the analysis of the weak gravitational lensing effect, i.e. the distortion effect of gravity on the images of distant galaxies. We propose a thresholding procedure based upon the (mixed) spin needlets construction recently advocated by Geller and Marinucci (2008, 2010) and Geller et al. (2008, 2009), and we investigate their rates of convergence and their adaptive properties over spin Besov balls.Spin fiber bundles Mixed spin needlets Adaptive nonparametric regression Thresholding Spin Besov spaces