Related papers: Function Based Nonlinear Least Squares and Applica…

In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…

Separable nonlinear least squares (SNLS)problem is a special class of nonlinear least squares (NLS)problems, whose objective function is a mixture of linear and nonlinear functions. It has many applications in many different areas,…

The non-linear corrections (NLC) to the longitudinal structure function in a limited approach is derived at low values of the Bjorken variable $x$ by using the Laplace transforms technique. The non-linear behavior of the longitudinal…

Power system state estimation (PSSE) is commonly formulated as weighted least-square (WLS) algorithm and solved using iterative methods such as Gauss-Newton methods. However, iterative methods have become more sensitive to system operating…

Linearization of power flow is an important topic in power system analysis. The computational burden can be greatly reduced under the linear power flow model while the model error is the main concern. Therefore, various linear power flow…

We propose a two-stage estimation method of variance components in time series models known as FDSLRMs, whose observations can be described by a linear mixed model (LMM). We based estimating variances, fundamental quantities in a time…

Latent structure methods, specifically linear continuous latent structure methods, are a type of fundamental statistical learning strategy. They are widely used for dimension reduction, regression and prediction, in the fields of…

This paper presents a generalization of the "weighted least-squares" (WLS), named "weighted pairing least-squares" (WPLS), which uses a rectangular weight matrix and is suitable for data alignment problems. Two fast solving methods,…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

A nonparametric model using a sequence of Bernstein polynomials is constructed to approximate arbitrary isotropic covariance functions valid in $\mathbb{R}^\infty$ and related approximation properties are investigated using the popular…

In this article, the parameters of a hybrid log-linear model (log-Poisson) are estimated using the fuzzy least-squares (FLS) procedures (Celmi\c{n}\v{s}, 987a,b, D'Urso and Gastaldi, 2000, DUrso and Gastaldi, 2001). A goodness of fit have…

This letter proposes a novel and highly efficient distribution system state estimation (DSSE) algorithm with nonlinear measurements from supervisory control and data acquisition (SCADA) systems. Conventional DSSE, i.e., a weighted least…

Developing efficient methods for solving parametric partial differential equations is crucial for addressing inverse problems. This work introduces a Least-Squares-based Neural Network (LS-Net) method for solving linear parametric PDEs. It…

Accurately monitoring the system's operating point is central to the reliable and economic operation of an electric power grid. Power system state estimation (PSSE) aims to obtain complete voltage magnitude and angle information at each bus…

This paper studies adaptive first-order least-squares finite element methods for second-order elliptic partial differential equations in non-divergence form. Unlike the classical finite element method which uses weak formulations of PDEs…

This work proposes a low complexity nonlinearity model and develops adaptive algorithms over it. The model is based on the decomposable---or rank-one, in tensor language---Volterra kernels. It may also be described as a product of FIR…

Multiple penalized least squares (MPLS) models are a flexible approach to find adaptive least squares solutions required to be simultaneously sparse and smooth. This is particularly important when addressing real-life inverse problems where…

The finite-dimensional parameters of the monotone single index model are often estimated by minimization of a least squares criterion and reparametrization to deal with the non-unicity. We avoid the reparametrization by using a…

People employ the function-on-function regression to model the relationship between two random curves. Fitting this model, widely used strategies include algorithms falling into the framework of functional partial least squares (typically…

Standard system identification methods often provide inconsistent estimates with closed-loop data. With the prediction error method (PEM), this issue is solved by using a noise model that is flexible enough to capture the noise spectrum.…