Difference between revisions of "Analyze data with the Statistics software R"

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* radius-minimax estimator: green (optimally robust; cf. Rieder et al. (2008))<br /><br />
 
* radius-minimax estimator: green (optimally robust; cf. Rieder et al. (2008))<br /><br />
 
By changing the y-position of the four movable points you should recognize the instability (non-robustness) of mean and standard deviation in contrast to the robust estimates; e.g., move one of the four movable points to the top of the plot.<br /><br />
 
By changing the y-position of the four movable points you should recognize the instability (non-robustness) of mean and standard deviation in contrast to the robust estimates; e.g., move one of the four movable points to the top of the plot.<br /><br />
<html>
 
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
 
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
 
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
 
<div id="jxgbox" class="jxgbox" style="width:700px; height:400px;" onmouseup="doIt();"></div>
 
</html>
 
 
===Online results:===
 
===Online results:===
 +
<html><script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script></html>
 
<pre id='output'>Statistics:<br></pre>
 
<pre id='output'>Statistics:<br></pre>
<html>
+
<jsxgraph width="700" height="400">
<script language="JavaScript">
+
         brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-0.15, 60, 11.15, -20],axis:true});
         brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 20, originY: 300, unitX: 60, unitY: 5,axis:true});
 
 
         brd.suspendUpdate();
 
         brd.suspendUpdate();
 
         var graph1,graph2,graph3,graph4,graph5,graph6,graph7,graph8,graph9;
 
         var graph1,graph2,graph3,graph4,graph5,graph6,graph7,graph8,graph9;
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                 }});
 
                 }});
 
         }
 
         }
</script>
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</jsxgraph>
</html>
 
  
 
=== The underlying source code ===
 
=== The underlying source code ===

Revision as of 11:11, 7 June 2011

Normal Location and Scale

This litte application sends the y-coordinates of the points which are normal distributed (pseudo-)random numbers to the server.
There, location and scale of the sample are estimated using the Statistics software R.
The return values are plotted and displayed.

The computed estimates are:

  • mean, standard deviation: red (non-robust!)
  • median and MAD: black (most-robust!)
  • radius-minimax estimator: green (optimally robust; cf. Rieder et al. (2008))

By changing the y-position of the four movable points you should recognize the instability (non-robustness) of mean and standard deviation in contrast to the robust estimates; e.g., move one of the four movable points to the top of the plot.

Online results:

Statistics:<br>

The underlying source code

The underlying JavaScript and PHP code

The R script can be downloaded here.

References

  • The Costs of not Knowing the Radius, Helmut Rieder, Matthias Kohl and Peter Ruckdeschel, Statistical Methods and Application 2008 Feb; 17(1): p.13-40; cf. also [1] for an extended version.
  • Robust Asymptotic Statistics, Helmut Rieder, Springer, 1994.
  • Numerical Contributions to the Asymptotic Theory of Robustness, Matthias Kohl, PhD-Thesis, University of Bayreuth, 2005; cf. also [2].

External links