Least-squares estimation of a convex discrete distribution

Convex Total Least Squares

We study the total least squares (TLS) problem that generalizes least squares regression by allowing measurement errors in both dependent and independent variables. TLS is widely used in applied fields including computer vision, system identification and econometrics. The special case when all dependent and independent variables have the same level of uncorrelated Gaussian noise, known as ordin...

On convex least squares estimation when the truth is linear.

We prove that the convex least squares estimator (LSE) attains a n-1/2 pointwise rate of convergence in any region where the truth is linear. In addition, the asymptotic distribution can be characterized by a modified invelope process. Analogous results hold when one uses the derivative of the convex LSE to perform derivative estimation. These asymptotic results facilitate a new consistent test...

Modified Weighted Least Squares Method to Improve Active Distribution System State Estimation

The development of communications and telecommunications infrastructure, followed by the extension of a new generation of smart distribution grids, has brought real-time control of distribution systems to electrical industry professionals’ attention. Also, the increasing use of distributed generation (DG) resources and the need for participation in the system voltage control, which is possible ...

Nonlinear Least Squares Estimation of the Shifted Gompertz Distribution

The focus of this paper is the existence of the best nonlinear least squares estimate for the shifted Gompertz distribution. As a main result, two theorems on the existence of the least squares estimate are obtained, as well as their generalization in the lp norm (1 ≤ p <∞). 2010 Mathematics Subject Classifications: 65D10, 65C20, 62J02

Least Squares Estimation