Related papers: Linear Source Apportionment using Generalized Leas…
Analyses of spectral data often assume a linear mixing hypothesis, which states that the spectrum of a mixed substance is approximately the mixture of the individual spectra of its constituent parts. We evaluate this hypothesis in the…
We consider the least-squares finite element method (lsfem) for systems of nonlinear ordinary differential equations and establish an optimal error estimate for this method when piecewise linear elements are used. The main assumptions are…
The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the…
Source apportionment analysis, which aims to quantify the attribution of observed concentrations of multiple air pollutants to specific sources, can be formulated as a non-negative matrix factorization (NMF) problem. However, NMF is…
We develop a framework for localized source detection in dynamical systems governed by nonlinear partial differential equations based on first and second-order sensitivity analysis. Building on the standard adjoint formulation, which…
In many applications it is important to estimate a fluid flow field from limited and possibly corrupt measurements. Current methods in flow estimation often use least squares regression to reconstruct the flow field, finding the…
We use location model methodology to guide the least squares analysis of the Lasso problem of variable selection and inference. The nuisance parameter is taken to be an indicator for the selection of explanatory variables and the interest…
Air sensor networks provide hyperlocal, high temporal resolution data on multiple pollutants that can support credible identification of common pollution sources. Source apportionment using least squares-based non-negative matrix…
A distributed adaptive algorithm is proposed to solve a node-specific parameter estimation problem where nodes are interested in estimating parameters of local interest, parameters of common interest to a subset of nodes and parameters of…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
Understanding the sources that contribute to fine particulate matter (PM$_{2.5}$) is of crucial importance for designing and implementing targeted air pollution mitigation strategies. Determining what factors contribute to a pollutant's…
Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…
Distributed algorithms, particularly Diffusion Least Mean Square, are widely favored for their reliability, robustness, and fast convergence in various industries. However, limited observability of the target can compromise the integrity of…
This is a brief tutorial on the least square estimation technique that is straightforward yet effective for parameter estimation. The tutorial is focused on the linear LSEs instead of nonlinear versions, since most nonlinear LSEs can be…
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…
Demixing problems in many areas such as hyperspectral imaging and differential optical absorption spectroscopy (DOAS) often require finding sparse nonnegative linear combinations of dictionary elements that match observed data. We show how…
Variance partitioning methods, which are built upon multivariate statistics, have been widely applied in different taxa and habitats in community ecology. Here, I performed a literature review on the development and application of the…
We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
We consider a resampling scheme for parameters estimates in nonlinear regression models. We provide an estimation procedure which recycles, via random weighting, the relevant parameters estimates to construct consistent estimates of the…