Sheep in Wolf’s clothing: Using the least squares criterion for quantile estimation

Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion

The aim of physical sciences is to discover the minimal set of parameters which completely describe physical systems and the laws relating the values of these parameters to the results of any set of measurements on the system. A coherent set of such laws is named a physical theory. To the extent that the values of the parameters can only be obtained as a results of measurements, one may equival...

Using the eigenvalue relaxation for binary least-squares estimation problems

The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact constraint and as such, is a convex problem with polynomial time complexity. Moreover, as a main pratical advantage of this relaxation over the standard Sem...

Robust Estimation Using Least Trimmed Squares

A robust procedure is proposed, starting from least trimmed squares as the initial estimator. The asymptotic distribution of the two-step and multi-step estimators is derived. This allows the use with a pre-specified efficiency under normality. It is argued that the good performance, together with the simplicity of the procedure, should make this the robust estimator of choice for applied work.

Nonparametric regression estimation using penalized least squares

We present multivariate penalized least squares regression estimates. We use Vapnik{ Chervonenkis theory and bounds on the covering numbers to analyze convergence of the estimates. We show strong consistency of the truncated versions of the estimates without any conditions on the underlying distribution.

Least Squares Estimation