Related papers: Restricted distance-type Gaussian estimators based…
In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed, where the defining convex function has an exponential nature. These estimators avoid the necessity of using an intermediate kernel…
Many modern products exhibit high reliability, often resulting in long times to failure. Consequently, conducting experiments under normal operating conditions may require an impractically long duration to obtain sufficient failure data for…
From the perspective of data reduction, the notions of minimal sufficient and complete statistics together play an important role in determining optimal statistics (estimators). The classical notion of sufficiency and completeness are not…
Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…
The authors consider the problem of estimating the density $g$ of independent and identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$, $\epsilon$ is a noise…
In this paper, we aim to design and analyze distributed Bayesian estimation algorithms for sensor networks. The challenges we address are to (i) derive a distributed provably-correct algorithm in the functional space of probability…
We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…
The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…
This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a…
While robust divergence such as density power divergence and $\gamma$-divergence is helpful for robust statistical inference in the presence of outliers, the tuning parameter that controls the degree of robustness is chosen in a…
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…
This paper discusses minimum distance estimation method in the linear regression model with dependent errors which are strongly mixing. The regression parameters are estimated through the minimum distance estimation method, and asymptotic…
We study the problem of bivariate discrete or continuous probability density estimation under low-rank constraints.For discrete distributions, we assume that the two-dimensional array to estimate is a low-rank probability matrix. In the…
In this article, we study a robust estimation method for a general class of integer-valued time series models. The conditional distribution of the process belongs to a broad class of distribution and unlike classical autoregressive…
This paper introduces a robust estimation framework based solely on the copula function. We begin by introducing a family of divergence measures tailored for copulas, including the \(\alpha\)-, \(\beta\)-, and \(\gamma\)-copula divergences,…
We consider the estimation of sensitivity indices based on divergence measures such as Hellinger distance. For sensitivity analysis of complex models, these divergence-based indices can be estimated by Monte-Carlo sampling (MCS) in…
Reliable inference from complex survey samples can be derailed by outliers and high-leverage observations induced by unequal inclusion probabilities and calibration. We develop a minimum Hellinger distance estimator (MHDE) for parametric…
Due to its heavy-tailed and fully parametric form, the multivariate generalized Gaussian distribution (MGGD) has been receiving much attention for modeling extreme events in signal and image processing applications. Considering the…
Gaussian Graphical Models (GGMs) are widely used to infer conditional dependence structures in high-dimensional data. However, standard precision matrix estimators are highly sensitive to data contamination, such as extreme outliers and…
As the most fundamental problem in statistics, robust location estimation has many prominent solutions, such as the trimmed mean, Winsorized mean, Hodges Lehmann estimator, Huber M estimator, and median of means. Recent studies suggest that…