Related papers: The Multivariate $S_n$ Estimator
The support vector machine (SVM) has an asymptotic behavior that parallels that of the quasi-maximum likelihood estimator (QMLE) for binary outcomes generated by a binary choice model (BCM), although it is not a QMLE. We show that, under…
This paper proposes a robust classification model, based on support vector machine (SVM), which simultaneously deals with outliers detection and feature selection. The classifier is built considering the ramp loss margin error and it…
We mainly study the M-estimation method for the high-dimensional linear regression model, and discuss the properties of M-estimator when the penalty term is the local linear approximation. In fact, M-estimation method is a framework, which…
We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting. Such models form a rich class of non-linear models with applications to signal processing, machine…
This work introduces the Matrix Minimum Covariance Determinant (MMCD) method, a novel robust location and covariance estimation procedure designed for data that are naturally represented in the form of a matrix. Unlike standard robust…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
Maronna's and Tyler's $M$-estimators are among the most widely used robust estimators for scatter matrices. However, when the dimension of observations is relatively high, their performance can substantially deteriorate in certain…
A popular regularized (shrinkage) covariance estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward its grand mean. In this paper, a more general…
In this paper, we analyze the behavior of the multivariate symmetric uncertainty (MSU) measure through the use of statistical simulation techniques under various mixes of informative and non-informative randomly generated features.…
Subsampling is a widely used and effective approach for addressing the computational challenges posed by massive datasets. Substantial progress has been made in developing non-uniform, probability-based subsampling schemes that prioritize…
In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…
Support Vector Machine (SVM) stands out as a prominent machine learning technique widely applied in practical pattern recognition tasks. It achieves binary classification by maximizing the "margin", which represents the minimum distance…
The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
In this work, the estimation of the multivariate normal mean by different classes of shrinkage estimators is investigated. The risk associated with the balanced loss function is used to compare two estimators. We start by considering…
Multiple importance sampling (MIS) is an increasingly used methodology where several proposal densities are used to approximate integrals, generally involving target probability density functions. The use of several proposals allows for a…
Fine stratification is a popular design as it permits the stratification to be carried out to the fullest possible extent. Some examples include the Current Population Survey and National Crime Victimization Survey both conducted by the…
We demonstrate that a popular class of nonparametric mutual information (MI) estimators based on k-nearest-neighbor graphs requires number of samples that scales exponentially with the true MI. Consequently, accurate estimation of MI…
We propose a robust variable selection procedure using a divergence based M-estimator combined with a penalty function. It produces robust estimates of the regression parameters and simultaneously selects the important explanatory…
Stochastic Gradient Descent (SGD) is arguably the most important single algorithm in modern machine learning. Although SGD with unbiased gradient estimators has been studied extensively over at least half a century, SGD variants relying on…