Related papers: Bias Reduction for Sum Estimation
The measurement error with normal distribution is universal in applications. Generally, smaller measurement error requires better instrument and higher test cost. In decision making based on attribute values of objects, we shall select an…
We consider the problem of identifying, from its first $m$ noisy moments, a probability distribution on $[0,1]$ of support $k<\infty$. This is equivalent to the problem of learning a distribution on $m$ observable binary random variables…
We prove several new results on the Hamming weight of bounded uniform and small-bias distributions. We exhibit bounded-uniform distributions whose weight is anti-concentrated, matching existing concentration inequalities. This construction…
We propose a novel modular debiasing technique applicable to any discrete random source, addressing the fundamental challenge of reliably extracting high-quality randomness from inherently imperfect physical processes. The method involves…
We consider a robust estimation of linear regression coefficients. In this note, we focus on the case where the covariates are sampled from an $L$-subGaussian distribution with unknown covariance, the noises are sampled from a distribution…
The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…
The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. It is assumed that the pre-change distribution is known (accurately estimated), while the only information about the…
We consider some computationally efficient and provably correct algorithms with near-optimal sample-complexity for the problem of noisy non-adaptive group testing. Group testing involves grouping arbitrary subsets of items into pools. Each…
A circuit $\mathcal{C}$ samples a distribution $\mathbf{X}$ with an error $\epsilon$ if the statistical distance between the output of $\mathcal{C}$ on the uniform input and $\mathbf{X}$ is $\epsilon$. We study the hardness of sampling a…
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…
Bayesian analysis plays a crucial role in estimating distribution of unknown parameters for given data and model. Due to the curse of dimensionality, it becomes difficult for high-dimensional problems, especially when multiple modes exist.…
Uniformity testing is one of the most well-studied problems in property testing, with many known test statistics, including ones based on counting collisions, singletons, and the empirical TV distance. It is known that the optimal sample…
An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…
We study the basic task of mean estimation in the presence of mean-shift contamination. In the mean-shift contamination model, an adversary is allowed to replace a small constant fraction of the clean samples by samples drawn from…
Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…
Noise is the defining feature of the NISQ era, but it remains unclear if noisy quantum devices are capable of quantum speedups. Quantum supremacy experiments have been a major step forward, but gaps remain between the theory behind these…
The recently proposed statistical finite element (statFEM) approach synthesises measurement data with finite element models and allows for making predictions about the unknown true system response. We provide a probabilistic error analysis…
Quantum sensors can potentially achieve the Heisenberg limit of sensitivity over a large dynamic range using quantum algorithms. The adaptive phase estimation algorithm (PEA) is one example that was proven to achieve such high sensitivities…
We prove several new results about bounded uniform and small-bias distributions. A main message is that, small-bias, even perturbed with noise, does not fool several classes of tests better than bounded uniformity. We prove this for…
This article studies the \emph{robust covariance matrix estimation} of a data collection $X = (x_1,\ldots,x_n)$ with $x_i = \sqrt \tau_i z_i + m$, where $z_i \in \mathbb R^p$ is a \textit{concentrated vector} (e.g., an elliptical random…