Difference between revisions of "Analyze data with the Statistics software R"
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* mean, standard deviation: red (non-robust!)<br /> | * mean, standard deviation: red (non-robust!)<br /> | ||
* median and MAD: black (most-robust!)<br /> | * median and MAD: black (most-robust!)<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> | <html> | ||
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t += p[i].Y() + ';'; | t += p[i].Y() + ';'; | ||
} | } | ||
| − | new Ajax.Request('/~ | + | new Ajax.Request('/~mkohl/rserv.php', { |
method:'post', | method:'post', | ||
parameters:'input='+escape(t), | parameters:'input='+escape(t), | ||
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graph3 = brd.createElement('curve', [[x[0],x[x.length-1]],[m+sd,m+sd]], {strokecolor:'red',dash:2}); | graph3 = brd.createElement('curve', [[x[0],x[x.length-1]],[m+sd,m+sd]], {strokecolor:'red',dash:2}); | ||
graph4 = brd.createElement('curve', [[x[0],x[x.length-1]],[m-sd,m-sd]], {strokecolor:'red',dash:2}); | graph4 = brd.createElement('curve', [[x[0],x[x.length-1]],[m-sd,m-sd]], {strokecolor:'red',dash:2}); | ||
| − | graph5 = brd.createElement('curve', [[x[0],x[x.length-1]],[med,med]], {strokecolor:' | + | graph5 = brd.createElement('curve', [[x[0],x[x.length-1]],[med,med]], {strokecolor:'black'}); |
graph1 = brd.createElement('curve', [[x[0],x[x.length-1]],[med-mad,med-mad]], {strokecolor:'black',dash:3}); | graph1 = brd.createElement('curve', [[x[0],x[x.length-1]],[med-mad,med-mad]], {strokecolor:'black',dash:3}); | ||
graph6 = brd.createElement('curve', [[x[0],x[x.length-1]],[med+mad,med+mad]], {strokecolor:'black',dash:3}); | graph6 = brd.createElement('curve', [[x[0],x[x.length-1]],[med+mad,med+mad]], {strokecolor:'black',dash:3}); | ||
Revision as of 12:33, 17 December 2008
Contents
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].
