Related papers: Bandlet Image Estimation with Model Selection
The change-plane Cox model is a popular tool for the subgroup analysis of survival data. Despite the rich literature on this model, there has been limited investigation into the asymptotic properties of the estimators of the…
We consider multiscale stochastic dynamical systems. In this article an \emph{intermediate} reduced model is obtained for a slow-fast system with fast mode driven by white noise. First, the reduced stochastic system on exponentially…
This paper presents a new perspective on the identification at infinity for the intercept of the sample selection model as identification at the boundary via a transformation of the selection index. This perspective suggests generalizations…
Wavelet shrinkage estimators are widely applied in several fields of science for denoising data in wavelet domain by reducing the magnitudes of empirical coefficients. In nonparametric regression problem, most of the shrinkage rules are…
Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real…
We provide a statistical analysis of the ability of digitized continuous shearlet systems to detect objects embedded in white noise. We analyze the possibility to subsample the shearlet transform and obtain a subset of significantly reduced…
Estimating expected polynomials of density functions from samples is a basic problem with numerous applications in statistics and information theory. Although kernel density estimators are widely used in practice for such functional…
This paper offers a new approach to address the model uncertainty in (potentially) divergent-dimensional single-index models (SIMs). We propose a model-averaging estimator based on cross-validation, which allows the dimension of covariates…
The detection and estimation of signals in noisy, limited data is a problem of interest to many scientific and engineering communities. We present a computationally simple, sample eigenvalue based procedure for estimating the number of…
All techniques for denoising involve a notion of a true (noise-free) image, and a hypothesis space. The hypothesis space may reconstruct the image directly as a grayscale valued function, or indirectly by its Fourier or wavelet spectrum.…
Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a…
This paper considers the asymptotic behavior in $\beta$-H\"older spaces, and under $L^p$ losses, of a Dirichlet kernel density estimator proposed by Aitchison and Lauder (1985) for the analysis of compositional data. In recent work, Ouimet…
Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…
We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded…
It is of particular interest to reconstruct or estimate bandlimited graph signals, which are smoothly varying signals defined over graphs, from partial noisy measurements. However, choosing an optimal subset of nodes to sample is NP-hard.…
Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…
We present a general M-estimation framework for inference on the wavelet variance. This framework generalizes the results on the scale-wise properties of the standard estimator and extends them to deliver the joint asymptotic properties of…
We consider the regression model with (known) random design. We investigate the minimax performances of an adaptive wavelet block thresholding estimator under the $\mathbb{L}^p$ risk with $p\ge 2$ over Besov balls. We prove that it is near…
We study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. We develop an asymptotically…
The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact…