View source for Shift parameter

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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====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  I.A. Ibragimov,   R.Z. [R.Z. Khas'minskii] Has'minskii,   "Statistical estimation: asymptotic theory" , Springer  (1981)  (Translated from Russian)</TD></TR></table>

====Comments====
This parameter is also called a location parameter.