the main purpose of this article is to increase the efficiency of the least squares method in numerical solution of ill-posed functional and physical equations. determining the least squares of a given function in an arbitrary set is often an ill-posed problem. in this article, by defining artificial constraint and using lagrange multipliers method, the attempt is to turn -dimensional least squ...

recently, in order to increase the efficiency of least squares method in numerical solution of ill-posed problems, the chain least squares method is presented in a recurrent process by babolian et al. despite the fact that the given method has many advantages in terms of accuracy and stability, it does not have any stopping criterion and has high computational cost. in this article, the attempt...

The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the vector b and/or the matrix A such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to b, while in data least squares (DLS) it is restricted to A. In scaled total least squares (Scaled TLS) [15], corrections to both b and A are allowed, ...

We investigate in this paper a variety of equalities for the ordinary least-squares estimators and the best linear unbiased estimators under the general linear (Gauss-Markov) model {y, Xβ, σΣ} and the restrained model {y, Xβ |Aβ = b, σΣ}.

Suppose we observe an ergodic Markov chain on the real line, with a parametric model for the autoregression function, i.e. the conditional mean of the transition distribution. If one speciies, in addition, a paramet-ric model for the conditional variance, one can deene a simple estimator for the parameter, the maximum quasi-likelihood estimator. It is robust against misspeciication of the condi...

We estimate the effect of changes in incarceration rates on changes in crime rates using state-level panel data. We develop an instrument for future changes in incarceration rates based on the theoretically predicted dynamic adjustment path of the aggregate incarceration rate in response to a shock to prison entrance or exit transition probabilities. Given that incarceration rates adjust to per...

This paper deals with an application of regression analysis to the regulation of the blood-sugar under diabetes mellitus. Section 2 gives a description of Gram-Schmidt orthogonalization, while Section 3 discusses the difference between Gauss-Markov estimation and Least Squares Estimation. Section 4 is devoted to the statistical analysis of the blood-sugar during the night. The response change o...

two multivariate calibration methods are compared for the simultaneous chromatographic determination and separation of sulfamethoxazole (smx) and phthalazine (phz) by high performance liquid chromatography (hplc). multivariate calibration techniques such as classical least squares (cls) and inverse least squares (ils) were introduced into hplc to determine the quantification by using uv detecto...