Related papers: An improved estimator for population mean using au…
Distributed statistical inference has recently attracted enormous attention. Many existing work focuses on the averaging estimator. We propose a one-step approach to enhance a simple-averaging based distributed estimator. We derive the…
The comparison of subnational areas is ubiquitous but survey samples of these areas are often biased or prohibitively small. Researchers turn to methods such as multilevel regression and poststratification (MRP) to improve the efficiency of…
We consider the estimation of a scalar parameter, when two estimators are available. The first is always consistent. The second is inconsistent in general, but has a smaller asymptotic variance than the first, and may be consistent if an…
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…
To take sample biases and skewness in the observations into account, practitioners frequently weight their observations according to some marginal distribution. The present paper demonstrates that such weighting can indeed improve the…
We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they…
It is well-known that trimmed sample means are robust against heavy tails and data contamination. This paper analyzes the performance of trimmed means and related methods in two novel contexts. The first one consists of estimating…
In this paper, we consider the distributed mean estimation problem where the server has access to some side information, e.g., its local computed mean estimation or the received information sent by the distributed clients at the previous…
When dealing with very large datasets of functional data, survey sampling approaches are useful in order to obtain estimators of simple functional quantities, without being obliged to store all the data. We propose here a Horvitz--Thompson…
Estimation of the population total of a variable can be improved by calibration on a set of auxiliary variables. It is difficult to establish that such a set of variables is sufficient, that estimation could not be improved by calibration…
Finite-sample upper bounds on the estimation error of a winsorized mean estimator of the population mean in the presence of heavy tails and adversarial contamination are established. In comparison to existing results, the winsorized mean…
Estimation and inference on causal parameters is typically reduced to a generalized method of moments problem, which involves auxiliary functions that correspond to solutions to a regression or classification problem. Recent line of work on…
This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…
This paper considers the problem of estimation of the Fisher information for location from a random sample of size $n$. First, an estimator proposed by Bhattacharya is revisited and improved convergence rates are derived. Second, a new…
We introduce a new sufficient statistic for the population parameter vector by allowing for the sampling design to first be selected at random amongst a set of candidate sampling designs. In contrast to the traditional approach in survey…
The moment conditions or estimating equations for instrumental variables quantile regression involve the discontinuous indicator function. We instead use smoothed estimating equations (SEE), with bandwidth $h$. We show that the mean squared…
This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…
We use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked,…
In this paper, we have established a new framework of truncated inverse sampling for estimating mean values of non-negative random variables such as binomial, Poisson, hyper-geometrical, and bounded variables. We have derived explicit…
We propose an estimator for the mean of a random vector in $\mathbb{R}^d$ that can be computed in time $O(n^4+n^2d)$ for $n$ i.i.d.~samples and that has error bounds matching the sub-Gaussian case. The only assumptions we make about the…