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Measurement error occurs when a covariate influencing a response variable is corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and…
We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with $O(n^2)$ linear constraints ($n$ being the sample size), is difficult to…
In this article we have suggested an improved estimator for estimating the population mean in simple random sampling using auxiliary information under the presence of measurement errors. The mean square error (MSE) of the proposed estimator…
Fr\'echet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables. However, its practical applicability has been hindered by its reliance on ideal scenarios with abundant and…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
We consider a linear regression model with a spatially correlated error term on a lattice. When estimating coefficients in the linear regression model, the generalized least squares estimator (GLSE) is used if the covariance structures are…
Contamination of covariates by measurement error is a classical problem in multivariate regression, where it is well known that failing to account for this contamination can result in substantial bias in the parameter estimators. The nature…
Compressed sensing is a signal processing technique in which data is acquired directly in a compressed form. There are two modeling approaches that can be considered: the worst-case (Hamming) approach and a statistical mechanism, in which…
The empirical Bayes estimators in mixed models are useful for small area estimation in the sense of increasing precision of prediction for small area means, and one wants to know the prediction errors of the empirical Bayes estimators based…
Machine learning models with both good predictability and high interpretability are crucial for decision support systems. Linear regression is one of the most interpretable prediction models. However, the linearity in a simple linear…
Regularized system identification has become a significant complement to more classical system identification. It has been numerically shown that kernel-based regularized estimators often perform better than the maximum likelihood estimator…
High-dimensional regression models with regularized sparse estimation are widely applied. For statistical inferences, debiased methods are available about single coefficients or predictions with sparse new covariate vectors (also called…
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…
In small area estimation different data sources are integrated in order to produce reliable estimates of target parameters (e.g., a mean or a proportion) for a collection of small subsets (areas) of a finite population. Regression models…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian…
The debiased estimator is a crucial tool in statistical inference for high-dimensional model parameters. However, constructing such an estimator involves estimating the high-dimensional inverse Hessian matrix, incurring significant…
We study semiparametric varying-coefficient partially linear models when some linear covariates are not observed, but ancillary variables are available. Semiparametric profile least-square based estimation procedures are developed for…
Estimation of a conditional mean (linking a set of features to an outcome of interest) is a fundamental statistical task. While there is an appeal to flexible nonparametric procedures, effective estimation in many classical nonparametric…
Given a full rank matrix $X$ with more columns than rows, consider the task of estimating the pseudo inverse $X^+$ based on the pseudo inverse of a sampled subset of columns (of size at least the number of rows). We show that this is…