The structure of a multivariate nonlinear regression model and properties of L ₂ estimators

Abstract

The nonlinear regression model

$$\begin{array}{*{20}{c}} {y = \eta \left( \vartheta \right) + \varepsilon ;\quad \left( {\vartheta \in \Theta } \right)} \\ {E\left( \varepsilon \right) = 0,\quad Var\left( \varepsilon \right) = {{\sigma }^{2}}W,} \\ \end{array}$$

considered in this chapter is multivariate, i.e. the vector of unknown parameters

$$\vartheta = \left( {{\vartheta _1}, \ldots ,{\vartheta _m}} \right)T$$

is multidimensional. It is assumed that ϑ ∈ Θ, and that the (known) parameter space Θ is a subset of R ^m such that

$$\Theta \subseteq \overline {\left( {\operatorname{int} \Theta } \right)} .$$