Parameter space

In statistics, parameter spaces are particularly useful for describing parametric families of probability distributions.

In the case of extremum estimators for parametric models, a certain objective function is maximized or minimized over the parameter space.

[1] Theorems of existence and consistency of such estimators require some assumptions about the topology of the parameter space.

For instance, compactness of the parameter space, together with continuity of the objective function, suffices for the existence of an extremum estimator.

Struik writes Thus the Klein quadric describes the parameters of lines in space.