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In this work, we study a random orthogonal projection based least squares estimator for the stable solution of a multivariate nonparametric regression (MNPR) problem. More precisely, given an integer $d\geq 1$ corresponding to the dimension…
We study the statistical properties of the least squares estimator in unimodal sequence estimation. Although closely related to isotonic regression, unimodal regression has not been as extensively studied. We show that the unimodal least…
To perform multiple regression, the least squares estimator is commonly used. However, this estimator is not robust to outliers. Therefore, robust methods such as S-estimation have been proposed. These estimators flag any observation with a…
In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced…
Unmeasured spatial confounding complicates exposure effect estimation in environmental health studies. This problem is exacerbated in studies with multiple health outcomes and environmental exposure variables, as the source and magnitude of…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a…
This paper reports on a novel template-free monocular non-rigid surface reconstruction approach. Existing techniques using motion and deformation cues rely on multiple prior assumptions, are often computationally expensive and do not…
We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…
Only learning one projection matrix from original samples to the corresponding binary labels is too strict and will consequentlly lose some intrinsic geometric structures of data. In this paper, we propose a novel transition subspace…
This paper presents an algorithm for indoor layout estimation and reconstruction through the fusion of a sequence of captured images and LiDAR data sets. In the proposed system, a movable platform collects both intensity images and 2D LiDAR…
LiDAR-camera systems have become increasingly popular in robotics recently. A critical and initial step in integrating the LiDAR and camera data is the calibration of the LiDAR-camera system. Most existing calibration methods rely on…
Iterative least-squares MR reconstructions typically use the Conjugate Gradient algorithm, despite known numerical issues. This paper demonstrates that the more recent LSMR algorithm has favourable numerical properties, and is to be…
In this paper, the problem of target localization in the presence of outlying sensors is tackled. This problem is important in practice because in many real-world applications the sensors might report irrelevant data unintentionally or…
We consider ordinary least squares estimation and variations on least squares estimation such as penalized (regularized) least squares and spectral shrinkage estimates for problems with p > n and associated problems with prediction of new…
Low-cost air pollution sensors, offering hyper-local characterization of pollutant concentrations, are becoming increasingly prevalent in environmental and public health research. However, low-cost air pollution data can be noisy, biased by…
We introduce the modified planar rotator method (MPRS), a physically inspired machine learning method for spatial/temporal regression. MPRS is a non-parametric model which incorporates spatial or temporal correlations via short-range,…
The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the…
In real data analysis with structural equation modeling, data are unlikely to be exactly normally distributed. If we ignore the non-normality reality, the parameter estimates, standard error estimates, and model fit statistics from normal…
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…