On Least Squares Estimation when the Dependent Variable is Grouped

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...

Mixing least-squares estimators when the variance is unknown

We propose a procedure to handle the problem of Gaussian regression when the variance is unknown. We mix least-squares estimators from various models according to a procedure inspired by that of Leung and Barron [IEEE Trans. Inform. Theory 52 (2006) 3396–3410]. We show that in some cases, the resulting estimator is a simple shrinkage estimator. We then apply this procedure to perform adaptive e...

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...