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Optimal Regression Design

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Introduction

There are a variety of problems in statistics, which demand the calculation of one or more probability distributions or measures. Optimal regression design is a particular example. Other examples include parameter estimation, adaptive design and stratified sampling.

Consider the problem of selecting an experimental design to furnish information on models of the type \(y \sim \pi (y\vert \underline{x},\underline{\theta },\sigma )\), where y is the response variable; \(\underline{x} = {({x}_{1},{x}_{2},\ldots ,{x}_{m})}^{T}\) are design variables, \(\underline{x}\) ∈ \(\mathcal{X}\) ⊆  m, \(\mathcal{X}\) is the design space; \(\underline{\theta }\) = \({({\theta }_{1},{\theta }_{2},\ldots ,{\theta }_{k})}^{T}\) are unknown parameters; σ is a nuisance parameter, fixed but unknown; and π(. ) is a probability model. In most applications, \(\mathcal{X}\) is taken to be compact. For each \(\underline{x}\) ∈ \(\mathcal{X}\), an experiment can be performed whose outcome is a...

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Mandal, S. (2011). Optimal Regression Design. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_647

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