Adaptive Methods

Introduction

Statistical procedures, the efficiencies of which are optimal and invariant with regard to the knowledge or not of certain features of the data, are called adaptive statistical methods.

Such procedures should be used when one suspects that the usual inference assumptions, for example, the normality of the error’s distribution, may not be met. Indeed, traditional methods have a serious defect. If the distribution of the error is non-normal, the power of classical tests, as pseudo-Gaussian tests, can be much less than the optimal power. So, the variance of the classical least squares estimator is much bigger than the smallest possible variance.

What Is Adaptivity?

The adaptive methods deal with the problem of estimating and testing hypotheses about a parameter of interest θ in the presence of nuisance parameter ν. The fact that ν remains unspecified induces, in general, a loss of efficiency with the situation where ν is exactly specified. Adaptivityoccurs when the loss of...