File:Hodges estimator risk function.svg

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Description
English: Risk function for the Hodges’ estimator, under the quadratic loss function
Date (UTC)
Source Own work
Author  // stpasha » 

Mathematica source code

[edit]
 f[n_, \[Theta]_] :=
   1/(2 Sqrt[\[Pi]]) \[ExponentialE]^(-Sqrt[n] - n \[Theta]^2)
     (\[ExponentialE]^(1/2 Sqrt[n] (-1 + n^(1/4) \[Theta])^2)
        (Sqrt[2] (1 + \[ExponentialE]^(2 n^(3/4) \[Theta])) n^(1/4) +
         2 \[ExponentialE]^(1/2 Sqrt[n] (1 + n^(1/4) \[Theta])^2) Sqrt[\[Pi]] -
         Sqrt[2] (-1 + \[ExponentialE]^(2 n^(3/4) \[Theta])) Sqrt[n] \[Theta]) +
   \[ExponentialE]^(Sqrt[n] + n \[Theta]^2) Sqrt[\[Pi]] (-1 + n \[Theta]^2)
     (Erf[(n^(1/4) - Sqrt[n] \[Theta])/Sqrt[2]] + Erf[(n^(1/4) + Sqrt[n] \[Theta])/Sqrt[2]]));
 Plot[{f[5, \[Theta]], f[50, \[Theta]], f[500, \[Theta]]}, {\[Theta], -2, 2},
      PlotRange -> All, PlotStyle -> Thickness[0.005]]

Licensing

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Public domain This work has been released into the public domain by its author, Stpasha. This applies worldwide.

In some countries this may not be legally possible; if so:
Stpasha grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Original upload log

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Transferred from en.wikipedia to Commons using For the Common Good.

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Date/Time Dimensions User Comment
01:05, 14 September 2010 512 × 512 (46,693 bytes) w:en:Stpasha (talk | contribs) ({{Information |Description = Risk function for the Hodges’ estimator, under the quadratic loss function |Source = I (~~~) created this work entirely by myself. |Date = ~~~~~ |Author = ~~~ |other_versions = }})

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current12:53, 15 September 2012Thumbnail for version as of 12:53, 15 September 2012512 × 512 (46 KB)Bulwersator (talk | contribs)Transferred from en.wikipedia: see original upload log above

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