Admissibility for Estimation with Quadratic Loss

Markov Chain Conditions for Admissibility in Estimation Problems with Quadratic Loss

Consider the problem of estimating a parametric function when the loss is quadratic. Given an improper prior distribution, there is a formal Bayes estimator for the parametric function. Associated with the estimation problem and the improper prior is a symmetric Markov chain. It is shown that if the Markov chain is recurrent, then the formal Bayes estimator is admissible. This result is used to...

Estimation with Quadratic Loss

It has long been customary to measure the adequacy of an estimator by the smallness of its mean squared error. The least squares estimators were studied by Gauss and by other authors later in the nineteenth century. A proof that the best unbiased estimator of a linear function of the means of a set of observed random variables is the least squares estimator was given by Markov [12], a modified ...

Shock Wave Admissibility for Quadratic Conservation Laws

In this work we present a new approach to the study of the stability of admissible shock wave solutions for systems of conservation laws that change type. The systems we treat have quadratic ux functions. We employ the fundamental wave manifold W as a global framework to characterize shock waves that comply with the viscosity admissibility criterion. Points of W parametrize dynamical systems as...

Density estimation with quadratic loss: a confidence intervals method

Regression with quadratic loss

Regression with quadratic loss is another basic problem studied in statistical learning theory. We have a random couple Z = (X ,Y ), where, as before, X is anRd -valued feature vector (or input vector) and Y is the real-valued response (or output). We assume that the unknown joint distribution P = PZ = PX Y of (X ,Y ) belongs to some class P of probability distributions over Rd ×R. The learning...