Sequential least-squares estimation and the electrical-network problem

Least Squares Estimation

Recursive Least Squares Estimation

We start with estimation of a constant based on several noisy measurements. Suppose we have a resistor but do not know its resistance. So we measure it several times using a cheap (and noisy) multimeter. How do we come up with a good estimate of the resistance based on these noisy measurements? More formally, suppose x = (x1, x2, . . . , xn) T is a constant but unknown vector, and y = (y1, y2, ...

Nonlinear Least-squares Estimation

The paper uses empirical process techniques to study the asymptotics of the least-squares estimator for the fitting of a nonlinear regression function. By combining and extending ideas of Wu and Van de Geer, it establishes new consistency and central limit theorems that hold under only second moment assumptions on the errors. An application to a delicate example of Wu’s illustrates the use of t...

Least Squares and Estimation Measures

Estimation of Backward Perturbation Bounds for Linear Least Squares Problem

Waldén, Karlson, and Sun found an elegant explicit expression of backward error for the linear least squares problem. However, it is difficult to compute this quantity as it involves the minimal singular value of certain matrix. In this paper we present a simple estimation to this bound which can be easily computed especially for large problems. Numerical results demonstrate the validity of the...