Related papers: Weighted shape-constrained estimation for the auto…

The paper introduces the weighted convolution, a novel approach to the convolution for signals defined on regular grids (e.g., 2D images) through the application of an optimal density function to scale the contribution of neighbouring…

Shape-constrained inference has wide applicability in bioassay, medicine, economics, risk assessment, and many other fields. Although there has been a large amount of work on monotone-constrained univariate curve estimation, multivariate…

We propose a focused weighted-average least squares (FWALS) estimator that addresses the computational burden of focused model averaging. By semi-orthogonalizing auxiliary regressors, the weighting problem is reduced from $2^{k_2}$…

Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…

We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight…

We develop a new approach for the estimation of a multivariate function based on the economic axioms of quasiconvexity (and monotonicity). On the computational side, we prove the existence of the quasiconvex constrained least squares…

We study kernel least-squares estimation under a norm constraint. This form of regularisation is known as Ivanov regularisation and it provides better control of the norm of the estimator than the well-established Tikhonov regularisation.…

In this paper we examine a novel way of imposing shape constraints on a local polynomial kernel estimator. The proposed approach is referred to as Shape Constrained Kernel-weighted Least Squares (SCKLS). We prove uniform consistency of the…

A novel regression method is introduced and studied. The procedure weights squared residuals based on their magnitude. Unlike the classic least squares which treats every squared residual equally important, the new procedure exponentially…

We propose a new class of spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a sparse structure for high-dimensional spatial panel dynamic models when panel members represent economic…

Weighted $\ell_1$-minimization has been studied as a technique for the reconstruction of a sparse signal from compressively sampled measurements when prior information about the signal, in the form of a support estimate, is available. In…

In the gravitational-wave analysis of pulsar-timing-array datasets, parameter estimation is usually performed using Markov Chain Monte Carlo methods to explore posterior probability densities. We introduce an alternative procedure that…

We investigate a weighted Multilevel Richardson-Romberg extrapolation for the ergodic approximation of invariant distributions of diffusions adapted from the one introduced in~[Lemaire-Pag\`es, 2013] for regular Monte Carlo simulation. In a…

Pre-trained vision foundation models (VFMs) provide strong semantic representations, yet their patch-level features are inherently coarse, limiting their effectiveness on tasks requiring fine-grained localization, dense prediction, and…

A weighted regression procedure is proposed for regression type problems where the innovations are heavy-tailed. This method approximates the least absolute regression method in large samples, and the main advantage will be if the sample is…

This paper provides a least squares formulation for the training of a 2-layer convolutional neural network using quadratic activation functions, a 2-norm loss function, and no regularization term. Using this method, an analytic expression…

We consider a high-probability non-asymptotic confidence estimation in the $\ell^2$-regularized non-linear least-squares setting with fixed design. In particular, we study confidence estimation for local minimizers of the regularized…

Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…

This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…

We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…