相关论文: Minimax Risk for Missing Mass Estimation

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…

Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…

The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…

In this paper, we study a generalized Kalman-Bucy filtering problem under uncertainty. The drift uncertainty for both signal process and observation process is considered and the attitude to uncertainty is characterized by a convex operator…

We consider an original problem that arises from the issue of security analysis of a power system and that we name optimal discovery with probabilistic expert advice. We address it with an algorithm based on the optimistic paradigm and on…

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 minimum mean-square error of the estimation of a signal where observed from the additive white Gaussian noise (WGN) channel's output, is analyzed. It is assumed that the channel input's signal is composed of a (normalized) sum of N…

We consider a Gaussian sequence model that contains ill-posed inverse problems as special cases. We assume that the associated operator is partially unknown in the sense that its singular functions are known and the corresponding singular…

Suppose we observe a Poisson process in real time for which the intensity may take on two possible values $\lambda_0$ and $\lambda_1$. Suppose further that the priori probability of the true intensity is not given. We solve a minimax…

We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different…

A general lower bound is developed for the minimax risk when estimating an arbitrary functional. The bound is based on testing two composite hypotheses and is shown to be effective in estimating the nonsmooth functional…

We study the problem of estimation of the value N_gamma(\theta) = sum(i=1)^d |\theta_i|^gamma for 0 < gamma <= 1 based on the observations y_i = \theta_i + \epsilon\xi_i, i = 1,...,d, where \theta = (\theta_1,...,\theta_d) are unknown…

In this article we have suggested an improved estimator for estimating the population mean in simple random sampling using auxiliary information under the presence of measurement errors. The mean square error (MSE) of the proposed estimator…

We consider the problem of choosing design parameters to minimize the probability of an undesired rare event that is described through the average of $n$ iid random variables. Since the probability of interest for near optimal design…

Knowledge of optimal quantum measurements is important for a wide range of situations, including quantum communication and quantum metrology. Quantum measurements are usually optimised with an ideal experimental realisation in mind. Real…

We develop a finite-sample optimal estimator for regression discontinuity design when the outcomes are bounded, including binary outcomes as the leading case. Our estimator achieves minimax mean squared error among linear shrinkage…

This paper considers probabilistic estimation of a low-rank matrix from non-linear element-wise measurements of its elements. We derive the corresponding approximate message passing (AMP) algorithm and its state evolution. Relying on…

Shrinkage methods are frequently used to improve the precision of least squares estimators of fixed effects. However, widely used shrinkage estimators guarantee improved precision only under strong distributional assumptions. I develop an…

We estimate convex polytopes and general convex sets in $\mathbb R^d,d\geq 2$ in the regression framework. We measure the risk of our estimators using a $L^1$-type loss function and prove upper bounds on these risks. We show that, in the…

Protection against disclosure is a legal and ethical obligation for agencies releasing microdata files for public use. Consider a microdata sample of size $n$ from a finite population of size $\bar{n}=n+\lambda n$, with $\lambda>0$, such…