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Shift parameter

From Encyclopedia of Mathematics
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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

[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.

How to Cite This Entry:
Shift parameter. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Shift_parameter&oldid=16795
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article