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The aim of this paper is to introduce new statistical criterions for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools…
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…
In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional…
This article investigates the least squares estimators (LSE) for the unknown parameters in stochastic differential equations (SDEs) that are affected by L\'evy noise, particularly when the sample paths are sparse. Specifically, given $n$…
The goal of regression is to recover an unknown underlying function that best links a set of predictors to an outcome from noisy observations. In nonparametric regression, one assumes that the regression function belongs to a pre-specified…
We consider the problem of signal estimation in a generalized linear model (GLM). GLMs include many canonical problems in statistical estimation, such as linear regression, phase retrieval, and 1-bit compressed sensing. Recent work has…
Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…
We study the optimal linear prediction of a random function that takes values in an infinite dimensional Hilbert space. We begin by characterizing the mean square prediction error (MSPE) associated with a linear predictor and discussing the…
Generalized estimating equations (GEE) are widely used to analyze longitudinal data; however, they are not appropriate for heteroscedastic data, because they only estimate regressor effects on the mean response{\textemdash}and therefore do…
Multiplicative errors in addition to spatially referenced observations often arise in geodetic applications, particularly in surface estimation with light detection and ranging (LiDAR) measurements. However, spatial regression involving…
We consider estimation and inference in a single index regression model with an unknown convex link function. We introduce a convex and Lipschitz constrained least squares estimator (CLSE) for both the parametric and the nonparametric…
Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs) is a fundamental yet computationally challenging problem arising in domains such as diagnosis, planning, and structured prediction. In many practical…
The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…
An empirical best linear unbiased prediction (EBLUP) estimator is utilized for efficient inference in small-area estimation. To measure its uncertainty, we need to estimate its mean squared error (MSE) since the true MSE cannot generally be…
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…
Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…
We address the problem of robust sparse estimation of the precision matrix for heavy-tailed distributions in high-dimensional settings. In such high-dimensional contexts, we observe that the covariance matrix can be approximated by a…
In this article, we study a partially linear single-index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases. A semiparametric estimation method based on a combination of…
We address the problem of estimating a random vector X from two sets of measurements Y and Z, such that the estimator is linear in Y. We show that the partially linear minimum mean squared error (PLMMSE) estimator does not require knowing…