$d$维环面上概率密度函数偏导数的非参数needlet估计

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 $X^\topβ$ is positive.The vectors $X$ and $β$ are independent and belong to the sphere $\mathbb{S}^{d-1}$ in $\mathbb{R}^{d}$.We prove lower bounds on the minimax risk for estimation of the density $f\_β$ over Besov bodies where the loss is a power of the $L^p(\mathbb{S}^{d-1})$ norm for $1\le p\le \infty$. We show that a hard thresholding estimator based on a needlet expansion with data-driven thresholds achieves these lower bounds up to logarithmic factors.

基于小波的球面上非参数异方差估计的自适应阈值处理

Adaptive thresholding for wavelet-based nonparametric heteroskedastic variance estimation on the sphere

研究单位球面上空间变化的异方差函数非参数估计问题，提出基于局部球面框架、结合硬阈值协议和样本分割方案的全数据驱动多分辨率估计器，证明其在标准损失函数下达到极小极大最优收敛率，有空间适应性，在多领域有潜在应用。

Block Thresholding on the Sphere

The aim of this paper is to study the nonparametric regression estimators on the sphere built by the needlet block thresholding. The block thresholding procedure proposed here follows the method introduced by Hall, Kerkyacharian and Picard in [Hall, Kerkyacharian, Picard, (1998), (1999)], modified to exploit the properties of the spherical standard needlets. Therefore, we will investigate on their convergence rates, attaining their adaptive properties over the Besov balls. This work is strongly motivated by issues arising in Cosmology and Astrophysics, concerning in particular the analysis of …

Adaptive global thresholding on the sphere

This work is concerned with the study of the adaptivity properties of nonparametric regression estimators over the $d$-dimensional sphere within the global thresholding framework. The estimators are constructed by means of a form of spherical wavelets, the so-called needlets, which enjoy strong concentration properties in both harmonic and real domains. The author establishes the convergence rates of the $L^p$-risks of these estimators, focussing on their minimax properties and proving their optimality over a scale of nonparametric regularity function spaces, namely, the Besov spaces.

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 $L^{2}$-risk function for these estimates, in particular its adaptivity, proving that its rate of convergence is nearly optimal.