Related papers: A Theory of Truncated Inverse Sampling
Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
Consider a Gaussian memoryless multiple source with $m$ components with joint probability distribution known only to lie in a given class of distributions. A subset of $k \leq m$ components are sampled and compressed with the objective of…
Variance estimation is important for statistical inference. It becomes non-trivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or sub-optimally handle these…
Truncated sum rules have been used to calculate the fundamental limits of the nonlinear susceptibilities; and, the results have been consistent with all measured molecules. However, given that finite-state models result in inconsistencies…
Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…
A substantial body of work in machine learning (ML) and randomized numerical linear algebra (RandNLA) has exploited various sorts of random sketching methodologies, including random sampling and random projection, with much of the analysis…
Thomas' partial likelihood estimator of regression parameters is widely used in the analysis of nested case-control data with Cox's model. This paper proposes a new estimator of the regression parameters, which is consistent and…
Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical…
A new nonparametric estimator of a convex regression function in any dimension is proposed and its convergence properties are studied. We start by using any estimator of the regression function and we \emph{convexify} it by taking the…
Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…
We review the alternative proposals introduced recently in the literature to update the standard formula to estimate the uncertainty on the mean of repeated measurements, and we compare their performances on synthetic examples with normal…
We propose a novel sequential Monte Carlo (SMC) method for sampling from unnormalized target distributions based on a reverse denoising diffusion process. While recent diffusion-based samplers simulate the reverse diffusion using…
An exact upper bound on the Winsorised-tilted mean of a symmetric random variable in terms of its second moment is given. Such results are used in work on nonuniform Berry--Esseen-type bounds for general nonlinear statistics.
Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…
This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator.…
We develop a tensor network-based method for calculating disorder-averaged expectation values in random spin chains without having to explicitly sample over disorder configurations. The algorithm exploits statistical translation invariance…
In this paper, we provide a general methodology to draw statistical inferences on individual signal coordinates or linear combinations of them in sparse phase retrieval. Given an initial estimator for the targeting parameter (some simple…
Network sampling is used around the world for surveys of vulnerable, hard-to-reach populations including people at risk for HIV, opioid misuse, and emerging epidemics. The sampling methods include tracing social links to add new people to…
We consider estimating the proportion of random variables for two types of composite null hypotheses: (i) the means or medians of the random variables belonging to a non-empty, bounded interval; (ii) the means or medians of the random…