Related papers: Fast Mean Estimation with Sub-Gaussian Rates
In this paper, we observe a sparse mean vector through Gaussian noise and we aim at estimating some additive functional of the mean in the minimax sense. More precisely, we generalize the results of (Collier et al., 2017, 2019) to a very…
We investigate the problem of representing information measures in terms of the moments of the underlying random variables. First, we derive polynomial approximations of the conditional expectation operator. We then apply these…
We provide a numerical scheme to approximate as closely as desired the Gaussian or exponential measure $\mu(\om)$ of (not necessarily compact) basic semi-algebraic sets$\om\subset\R^n$. We obtain two monotone (non increasing and non…
We study the problem of estimating the common mean $\mu$ of $n$ independent symmetric random variables with different and unknown standard deviations $\sigma_1 \le \sigma_2 \le \cdots \le\sigma_n$. We show that, under some mild regularity…
The author uses a Stein-type covariance identity to obtain moment estimators for the parameters of the quadratic polynomial subfamily of Pearson distributions. The asymptotic distribution of the estimators is obtained, and normality and…
Meta-analysis is widely used to integrate results from multiple experiments to obtain generalized insights. Since meta-analysis datasets are often heteroscedastic due to varying subgroups and temporal heterogeneity arising from experiments…
We obtain an optimal bound for a Gaussian approximation of a large class of vector-valued random processes. Our results provide a substantial generalization of earlier results that assume independence and/or stationarity. Based on the decay…
We use the Sum of Squares method to develop new efficient algorithms for learning well-separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that substantially improve upon the statistical guarantees achieved…
We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
In this article, we consider an imputation method to handle missing response values based on semiparametric quantile regression estimation. In the proposed method, the missing response values are generated using the estimated conditional…
Covariance estimation becomes challenging in the regime where the number p of variables outstrips the number n of samples available to construct the estimate. One way to circumvent this problem is to assume that the covariance matrix is…
We tackle the problem of the estimation of a vector of means from a single vector-valued observation $y$. Whereas previous work reduces the size of the estimates for the largest (absolute) sample elements via shrinkage (like James-Stein) or…
Random-effects meta-analysis requires an estimate of the between-study variance, $\tau^2$. We study methods of estimation of $\tau^2$ and its confidence interval in meta-analysis of odds ratio, and also the performance of related estimators…
In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…
In order to estimate the population mean in the presence of both non-response and measurement errors that are uncorrelated, the paper presents some novel estimators employing ranked set sampling by utilizing auxiliary information.Up to the…
We provide an efficient algorithm for the classical problem, going back to Galton, Pearson, and Fisher, of estimating, with arbitrary accuracy the parameters of a multivariate normal distribution from truncated samples. Truncated samples…
Let $Y$ be a Gaussian vector of $\mathbb{R}^n$ of mean $s$ and diagonal covariance matrix $\Gamma$. Our aim is to estimate both $s$ and the entries $\sigma_i=\Gamma_{i,i}$, for $i=1,...,n$, on the basis of the observation of two independent…
This article suggests an efficient class of estimators of population median of the study variable using an auxiliary variable. Asymptotic expressions of bias and mean square error of the proposed class of estimators have been obtained.…
In this paper we have suggested difference-type estimator for estimation of population mean of the study variable y in the presence of measurement error using auxiliary information. The optimum estimator in the suggested estimator has been…