Shift parameter

A parameter $ \theta $, $ \theta \in \Theta \subset \mathbf R ^ {k} $, of a family of functions $ \{ \phi _ \theta ( \cdot ) \} $ which are defined on $ \mathbf R ^ {k} $ by the formula

$$ \phi _ \theta ( \cdot ) = \phi ( \cdot - \theta ) \ \ \textrm{ for } \textrm{ any } \theta \in \Theta , $$

where $ \phi ( \cdot ) $ is a given function on $ \mathbf R ^ {k} $.

References

[1]	I.A. Ibragimov, R.Z. [R.Z. Khas'minskii] Has'minskii, "Statistical estimation: asymptotic theory" , Springer (1981) (Translated from Russian)

Comments

This parameter is also called a location parameter.