Theoretic research on robustified least squares estimator based on equivalent variance-covariance

Level Robust Methods Based on the Least Squares Regression Estimator

Least-Squares Covariance Matrix Adjustment

We consider the problem of finding the smallest adjustment to a given symmetric n × n matrix, as measured by the Euclidean or Frobenius norm, so that it satisfies some given linear equalities and inequalities, and in addition is positive semidefinite. This least-squares covariance adjustment problem is a convex optimization problem, and can be efficiently solved using standard methods when the ...

Covariance shaping least-squares estimation

A new linear estimator is proposed, which we refer to as the covariance shaping least-squares (CSLS) estimator, for estimating a set of unknown deterministic parameters x observed through a known linear transformation H and corrupted by additive noise. The CSLS estimator is a biased estimator directed at improving the performance of the traditional least-squares (LS) estimator by choosing the e...

Least-squares variance component estimation

Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible because it works with a userdefined weight matrix; and it is attractive because it allows one to directly apply the existing body of knowledge of L...

On Berry-Esseen type bound for least squares estimator for diffusion processes based on discrete observations

The paper is concerned with the distribution of the least squares estimator (LSE) of the drift parameter in the stochastic differential equation (SDE) of small diffusion observed over discrete set of time points. Convergence of the distribution of the least squares estimator to the standard normal distribution with an error bound has been obtained when the discretization step decreases with noi...