Analyze data with the Statistics software R: Difference between revisions

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                         var est2 = a[5]*1.0;
                         var est2 = a[5]*1.0;


console.log(t, res, m, sd, med, mad, est1, est2);
                         if (!graph2) {  
                         if (!graph2) {  
                             graph2 = brd.createElement('curve', [[x[0],x[x.length-1]],[m,m]], {strokecolor:'red'});  
                             graph2 = brd.createElement('curve', [[x[0],x[x.length-1]],[m,m]], {strokecolor:'red'});  
Line 115: Line 114:
                         }
                         }


                         $('output').innerHTML = '<b><font size="+1">Normal location and scale:</font></b><br /><br />'+  
                         document.getElementById('output').innerHTML = '<b><font size="+1">Normal location and scale:</font></b><br /><br />'+  
                                 '<b>Estimates for location (true value = 10):</b><br />' +
                                 '<b>Estimates for location (true value = 10):</b><br />' +
                                 'Mean = ' + brd.round(m,2) + '<br />' +
                                 'Mean = ' + Math.round(m,2) + '<br />' +
                                 'Median = ' + brd.round(med,2) + '<br />' +
                                 'Median = ' + Math.round(med,2) + '<br />' +
                                 'Radius-minimax estimator = ' + brd.round(est1,2) + '<br /><br />' +
                                 'Radius-minimax estimator = ' + Math.round(est1,2) + '<br /><br />' +
                                 '<b>Estimates for scale (true value = 3):</b><br />' +
                                 '<b>Estimates for scale (true value = 3):</b><br />' +
                                 'Standard deviation = ' + brd.round(sd,2) + '<br />' +
                                 'Standard deviation = ' + Math.round(sd,2) + '<br />' +
                                 'MAD = ' + brd.round(mad,2) + '<br />' +  
                                 'MAD = ' + Math.round(mad,2) + '<br />' +  
                                 'Radius-minimax estimator = ' + brd.round(est2,2) + '<br />';
                                 'Radius-minimax estimator = ' + Math.round(est2,2) + '<br />';
                         brd.update();
                         brd.update();
                     };
                     };

Revision as of 10:35, 21 February 2013

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

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