Parameter estimation method of Jelinski-Moranda (JM) model based on weighted nonlinear least squares (WNLS) is proposed. The formulae of resolving the parameter WNLS estimation (WNLSE) are derived, and the empirical weight function and heteroscedasticity problem are discussed. The effects of optimization parameter estimation selection based on maximum likelihood estimation (MLE) method, least s...

In this note, we present two results on the scaled total least squares problem. First, we discuss the relation between the scaled total least squares and the least squares problems. We derive an upper bound for the difference between the scaled total least squares solution and the least squares solution and establish a quantitative relation between the scaled total least squares residual and th...

The problem of oversampling parameter estimation for noisy sinusoidal signals is addressed. We first extend the weighted least squares (WLS) approach to the complex sinusoids. Then the oversampling weighted least squares (OSWLS) estimator is proposed based on data decimation. Estimation performance of the OSWLS method is analyzed via theoretical and simulation studies. Results are also compared...

Two weighted compression schemes, Weighted Least Squares (wLS) and Weighted Principal Component Analysis (wPCA), are compared by considering their performance in minimizing both spectral and colorimetric errors of reconstructed reflectance spectra. A comparison is also made among seven different weighting functions incorporated into ordinary PCA/LS to give selectively more importance to the wav...

The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the data to make the corrected system compatible. In ordinary least squares (LS) the correction is restricted to the right hand side b, while in scaled total least squares (Scaled TLS) [10; 7] corrections to both b and A are allowed, and their relative sizes are determined by a real positive...

Univariate partial least squares (PLS) is a method of modeling relationships between a Y variable and other explanatory vanables. It may be used with any number of explanatory variables, even far more than the number of observations. A simple interpretation is given that shows the method to be a straightforward and reasonable way of forming prediction equations. Its relationship to multivariate...

In this paper the meshless local Petrov-Galerkin (MLPG) method is implemented to study the buckling of isotropic cylindrical shells under axial load. Displacement field equations, based on Donnell and first order shear deformation theory, are taken into consideration. The set of governing equations of motion are numerically solved by the MLPG method in which according to a semi-inverse method, ...

The problem of oversampling parameter estimation for noisy sinusoidal signals is addressed. We first extend the weighted least squares (WLS) approach to the complex sinusoids. Then the oversampling weighted least squares (OSWLS) estimator is proposed based on data decimation. Estimation performance of the OSWLS method is analyzed via theoretical and simulation studies. Results are also compared...

In a linear model approach to the analysis of binary data, parameters of the model may be estimated by the method of maximum likelihood, or by weighted or unweighted least squares. The technique of generalized linear models permits maximum likelihood estimates of parameters to be obtained by iterative weighted least squares, with tests of significance based on analysis of deviance, a generaliza...

In this paper, we propose an approach for learning regression models efficiently in an environment where multiple features and data-points are added incrementally in a multistep process. At each step, any finite number of features maybe added and hence, the setting is not amenable to low rank updates. We show that our approach is not only efficient and optimal for ordinary least squares, weight...