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A parameter <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084910/s0849101.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084910/s0849102.png" />, of a family of functions <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084910/s0849103.png" /> which are defined on <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084910/s0849104.png" /> by the formula
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<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084910/s0849105.png" /></td> </tr></table>
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where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084910/s0849106.png" /> is a given function on <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084910/s0849107.png" />.
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A parameter  $  \theta $,
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$  \theta \in \Theta \subset  \mathbf R  ^ {k} $,
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of a family of functions  $  \{ \phi _  \theta  ( \cdot ) \} $
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which are defined on  $  \mathbf R  ^ {k} $
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by the formula
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$$
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\phi _  \theta  ( \cdot )  =  \phi ( \cdot - \theta ) \ \
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\textrm{ for }  \textrm{ any }  \theta \in \Theta ,
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$$
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where $  \phi ( \cdot ) $
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is a given function on $  \mathbf R  ^ {k} $.
  
 
====References====
 
====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>
 
<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>
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====Comments====
 
====Comments====
 
This parameter is also called a location parameter.
 
This parameter is also called a location parameter.

Latest revision as of 08:13, 6 June 2020


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=48685
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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