Related papers: Mean Estimation from One-Bit Measurements
Statistical agencies are often asked to produce small area estimates (SAEs) for positively skewed variables. When domain sample sizes are too small to support direct estimators, effects of skewness of the response variable can be large. As…
We revisit the problem of Gaussian mean testing in a distributed, communication constrained setting, where each of $n$ users independently observes samples from an unknown $d$-dimensional spherical Gaussian distribution…
We study the performance of a wide class of convex optimization-based estimators for recovering a signal from corrupted one-bit measurements in high-dimensions. Our general result predicts sharply the performance of such estimators in the…
We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…
By performing local projective measurements on a two-qubit entangled state one can certify in a device-independent way up to one bit of randomness. We show here that general measurements, defined by positive-operator-valued measures, can…
Estimation using pooled sampling has long been an area of interest in the group testing literature. Such research has focused primarily on the assumed use of fixed sampling plans (i), although some recent papers have suggested alternative…
The estimation of the amplitude of a sine wave from the sequence of its quantized samples is a typical problem in instrumentation and measurement. A standard approach for its solution makes use of a least squares estimator (LSE) that,…
We consider the problem where $n$ clients transmit $d$-dimensional real-valued vectors using $d(1+o(1))$ bits each, in a manner that allows the receiver to approximately reconstruct their mean. Such compression problems naturally arise in…
We present new fundamental results for the mean square error (MSE)-optimal conditional mean estimator (CME) in one-bit quantized systems for a Gaussian mixture model (GMM) distributed signal of interest, possibly corrupted by additive white…
We propose an improved estimator for the multi-task averaging problem, whose goal is the joint estimation of the means of multiple distributions using separate, independent data sets. The naive approach is to take the empirical mean of each…
This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role…
We study the approximation of expectations $\E(f(X))$ for Gaussian random elements $X$ with values in a separable Hilbert space $H$ and Lipschitz continuous functionals $f \colon H \to \R$. We consider restricted Monte Carlo algorithms,…
In this paper we develop a theory of matrix completion for the extreme case of noisy 1-bit observations. Instead of observing a subset of the real-valued entries of a matrix M, we obtain a small number of binary (1-bit) measurements…
Robust mean estimation is the problem of estimating the mean $\mu \in \mathbb{R}^d$ of a $d$-dimensional distribution $D$ from a list of independent samples, an $\epsilon$-fraction of which have been arbitrarily corrupted by a malicious…
A new bandwidth selection rule that uses different bandwidths for the local linear regression estimators on the left and the right of the cut-off point is proposed for the sharp regression discontinuity estimator of the mean program impact…
This article addresses the problem of estimating the population mean in the presence of auxiliary information when study variable itself is qualitative in nature. Bias and mean squared error (MSE) expressions of the class of estimators are…
We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…
We consider the problem of determining the optimal block (or subsample) size for a spatial subsampling method for spatial processes observed on regular grids. We derive expansions for the mean square error of the subsampling variance…
We study the problem of estimating a multivariate convex function defined on a convex body in a regression setting with random design. We are interested in optimal rates of convergence under a squared global continuous $l_2$ loss in the…
This paper regards randomized discrete-time consensus systems that preserve the average "on average". As a main result, we provide an upper bound on the mean square deviation of the consensus value from the initial average. Then, we apply…