相关论文: Minimax estimation with thresholding and its appli…

We investigate minimax estimators for quantum state tomography under general Bregman divergences. First, generalizing the work of Komaki et al. $\href{http://dx.doi.org/10.3390/e19110618}{\textrm{[Entropy 19, 618 (2017)]}}$ for relative…

In the measurement-constrained problems, despite the availability of large datasets, we may be only affordable to observe the labels on a small portion of the large dataset. This poses a critical question that which data points are most…

In experimental design, we are given a large collection of vectors, each with a hidden response value that we assume derives from an underlying linear model, and we wish to pick a small subset of the vectors such that querying the…

This paper is devoted to the multivariate estimation of a vector of Poisson means. A novel loss function that penalises bad estimates of each of the parameters and the sum (or equivalently the mean) of the parameters is introduced. Under…

This paper explores a class of empirical Bayes methods for level-dependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy-tailed…

This work is intended as a contribution to a wavelet-based adaptive estimator of the memory parameter in the classical semi-parametric framework for Gaussian stationary processes. In particular we introduce and develop the choice of a…

It has previously been shown that ordinary least squares can be used to estimate the coefficients of the single-index model under only mild conditions. However, the estimator is non-robust leading to poor estimates for some models. In this…

Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental problem in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Towards bridging…

We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…

We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…

MinMax sampling is a technique for downsampling a real-valued vector which minimizes the maximum variance over all vector components. This approach is useful for reducing the amount of data that must be sent over a constrained network link…

A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least favorable prior distribution. The Bayesian estimator induced by a least favorable prior,…

Quantum tomography requires repeated measurements of many copies of the physical system, all prepared by a source in the unknown state. In the limit of very many copies measured, the often-used maximum-likelihood (ML) method for converting…

The James-Stein estimator is an estimator of the multivariate normal mean and dominates the maximum likelihood estimator (MLE) under squared error loss. The original work inspired great interest in developing shrinkage estimators for a…

Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However,…

In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both…

We consider the problem of estimating the mean of a random vector based on i.i.d. observations and adversarial contamination. We introduce a multivariate extension of the trimmed-mean estimator and show its optimal performance under minimal…

We study the problem of estimating a mean pattern from a set of similar curves in the setting where the variability in the data is due to random geometric deformations and additive noise. We propose an estimator based on the notion of…

This paper considers the nonparametric regression model with negatively super-additive dependent (NSD) noise and investigates the convergence rates of thresholding estimators. It is shown that the term-by-term thresholding estimator…

We present a novel approach for nonparametric regression using wavelet basis functions. Our proposal, $\texttt{waveMesh}$, can be applied to non-equispaced data with sample size not necessarily a power of 2. We develop an efficient proximal…