Related papers: One-step Local M-estimator for Integrated Jump-Dif…
This study develops a non-asymptotic Gaussian approximation theory for distributions of M-estimators, which are defined as maximizers of empirical criterion functions. In existing mathematical statistics literature, numerous studies have…
We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing…
In this paper, we study properties of penalized and structured M-estimators of multivariate scatter, based on geodesically convex but not necessarily smooth penalty functions. Existence and uniqueness conditions for these penalized and…
Training-free diffusion priors enable inverse-problem solvers without retraining, but for nonlinear forward operators data consistency often relies on repeated derivatives or inner optimization/MCMC loops with conservative step sizes,…
A large dimensional characterization of robust M-estimators of covariance (or scatter) is provided under the assumption that the dataset comprises independent (essentially Gaussian) legitimate samples as well as arbitrary deterministic…
Bai (2010) and Bai et al. (2012) proposed robust mixture regression method based on the M regression estimation. However, the M-estimators are robust against the outliers in response variables, but they are not robust against the outliers…
This paper proposes an original approach to better understanding the behavior of robust scatter matrix $M$-estimators. Scatter matrices are of particular interest for many signal processing applications since the resulting performance…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors [El Karoui et al.,…
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…
Mutual information is a nonlinear measure used in time series analysis in order to measure the linear and non-linear correlations at any lag $\tau$. The aim of this study is to evaluate some of the most commonly used mutual information…
In this paper, we consider a piecewise deterministic Markov process (PDMP), with known flow and deterministic transition measure, and unknown jump rate $\lambda$. To estimate nonparametrically the jump rate, we first construct an adaptive…
The estimation of the frequencies of multiple superimposed exponentials in noise is an important research problem due to its various applications from engineering to chemistry. In this paper, we propose an efficient and accurate algorithm…
Nonresponse after probability sampling is a universal challenge in survey sampling, often necessitating adjustments to mitigate sampling and selection bias simultaneously. This study explored the removal of bias and effective utilization of…
We introduce a class of regularized M-estimators of multivariate scatter and show, analogous to the popular spatial sign covariance matrix (SSCM), that they possess high breakdown points. We also show that the SSCM can be viewed as an…
This paper is concerned with the detection of multiple change-points in the joint distribution of independent categorical variables. The procedures introduced rely on model selection and are based on a penalized least-squares criterion.…
Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a…
This paper proposes a robust and computationally efficient estimation framework for fitting parametric distributions based on trimmed L-moments. Trimmed L-moments extend classical L-moment theory by downweighting or excluding extreme order…
The parameters of the log-logistic distribution are generally estimated based on classical methods such as maximum likelihood estimation, whereas these methods usually result in severe biased estimates when the data contain outliers. In…
Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Furthermore, we propose several variants of…