Related papers: Mean Estimation from Adaptive One-bit Measurements
In this paper we consider the issue of reliability of measurements in distributed adaptive estimation problem. To this aim, we assume a sensor network with different observation noise variance among the sensors and propose new estimation…
We study the problem of private vector mean estimation in the shuffle model of privacy where $n$ users each have a unit vector $v^{(i)} \in\mathbb{R}^d$. We propose a new multi-message protocol that achieves the optimal error using…
Randomized approximation algorithms for many #P-complete problems (such as the partition function of a Gibbs distribution, the volume of a convex body, the permanent of a $\{0,1\}$-matrix, and many others) reduce to creating random…
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…
Let $(\{1,2,\ldots,n\},d)$ be a metric space. We analyze the expected value and the variance of $\sum_{i=1}^{\lfloor n/2\rfloor}\,d({\boldsymbol{\pi}}(2i-1),{\boldsymbol{\pi}}(2i))$ for a uniformly random permutation ${\boldsymbol{\pi}}$ of…
We study the problem of high-dimensional robust mean estimation in an online setting. Specifically, we consider a scenario where $n$ sensors are measuring some common, ongoing phenomenon. At each time step $t=1,2,\ldots,T$, the $i^{th}$…
In 1-bit compressed sensing, the aim is to estimate a $k$-sparse unit vector $x\in S^{n-1}$ within an $\epsilon$ error (in $\ell_2$) from minimal number of linear measurements that are quantized to just their signs, i.e., from measurements…
We investigate the asymptotic mean squared error of kernel estimators of the intensity function of a spatial point process. We show that when $n$ independent copies of a point process in $\mathbb R^d$ are superposed, the optimal bandwidth…
In this paper, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan (1973), who proved a Central Limit Theorem for the usual least square estimator…
In this paper we have suggested a family of estimators for the population mean in the presence of measurement errors. Expression for the mean squared error (MSE) of the suggested family is derived. An empirical study has been carried out to…
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…
Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in…
Estimators of information theoretic measures such as entropy and mutual information are a basic workhorse for many downstream applications in modern data science. State of the art approaches have been either geometric (nearest neighbor (NN)…
It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…
The present paper discusses the problem of estimating the finite population mean of study variable in simple random sampling in the presence of non response and response error together. The estimators in this article use auxiliary…
We study the problem of estimating the mean of a random vector in $\mathbb{R}^d$ based on an i.i.d.\ sample, when the accuracy of the estimator is measured by a general norm on $\mathbb{R}^d$. We construct an estimator (that depends on the…
This paper provides some useful tests for fitting a parametric single-index regression model when covariates are measured with error and validation data is available. We propose two tests whose consistency rates do not depend on the…
In this paper, we suggest an estimator using two auxiliary variables in stratified random sampling. The propose estimator has an improvement over mean per unit estimator as well as some other considered estimators. Expressions for bias and…
We study the problem of robustly estimating the mean or location parameter without moment assumptions. We show that for a large class of symmetric distributions, the same error as in the Gaussian setting can be achieved efficiently. The…
Multi-layer feedforward networks have been used to approximate a wide range of nonlinear functions. An important and fundamental problem is to understand the learnability of a network model through its statistical risk, or the expected…