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In this paper we propose a semi-parametric Bayesian Generalized Least Squares estimator. In a generic setting where each error is a vector, the parametric Generalized Least Square estimator maintains the assumption that each error vector…

Standard metrics of performance of classifiers, such as accuracy and sensitivity, do not reveal the trust or confidence in the predicted labels of data. While other metrics such as the computed probability of a label or the signed distance…

We introduce a general semiparametric clusterwise elliptical distribution to assess how latent cluster structure shapes continuous outcomes. Using a subjectwise representation, we first estimate cluster-specific mean vectors and a…

This paper presents a distributed estimator for a deterministic parametric physical field sensed by a homogeneous sensor network and develops a new transformed expression for the Cramer-Rao lower bound (CRLB) on the variance of distributed…

The Bayesian Cram\'er-Rao bound (CRB) provides a lower bound on the mean square error of any Bayesian estimator under mild regularity conditions. It can be used to benchmark the performance of statistical estimators, and provides a…

Simultaneous confidence bands (SCBs) for percentiles in linear regression are valuable tools with many applications. In this paper, we propose a novel criterion for comparing SCBs for percentiles, termed the Minimum Area Confidence Set…

Support Vector Machine (SVM) is a robust machine learning algorithm with broad applications in classification, regression, and outlier detection. SVM requires tuning the regularization parameter (RP) which controls the model capacity and…

While Cram\'er-Rao lower bound is an important metric in sensing functions in integrated sensing and communications (ISAC) designs, its optimization usually involves a computationally expensive solution such as semidefinite relaxation. In…

Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…

This chapter reviews methods for linear shrinkage of the sample covariance matrix (SCM) and matrices (SCM-s) under elliptical distributions in single and multiple populations settings, respectively. In the single sample setting a popular…

We consider a broad class of semiparametric regression models in which the conditional distribution of the response takes the form $f\{Y|\bf{x}^{\rm T}\boldsymbol{\beta}+m(z), \phi\}$, which is known up to a parametric component…

Elliptically symmetric distributions are a classic example of a semiparametric model where the location vector and the scatter matrix (or a parameterization of them) are the two finite-dimensional parameters of interest, while the density…

This work examines risk bounds for nonparametric distributional regression estimators. For convex-constrained distributional regression, general upper bounds are established for the continuous ranked probability score (CRPS) and the…

This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…

In many practical parameter estimation problems, such as coefficient estimation of polynomial regression, the true model is unknown and thus, a model selection step is performed prior to estimation. The data-based model selection step…

Clustering high-dimensional data is especially challenging when cluster distributions are heavy tailed and only approximately elliptical. Existing high-dimensional methods are largely built for Gaussian or other light-tailed models, whereas…

We consider distributed estimation of a Gaussian source in a heterogenous bandwidth constrained sensor network, where the source is corrupted by independent multiplicative and additive observation noises, with incomplete statistical…

The Cram\'er-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the…

We extend the traditional framework for estimating subspace bases that maximize the preserved signal energy to additionally preserve the Cram\'er-Rao bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and precision…

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…