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Conclusions of the simulation study

For the sake of comparison, we use the tex2html_wrap_inline1984 confidence interval, using the values obtained by simulation and presented in Table 1. Table 4 summarizes that information in the following way: every entry has either a ``Y'' or a ``N'', indicating weather the corresponding confidence interval for the estimator/distribution situation hits the true value (.5) or not. Also, the number ``(j)'' indicates that the corresponding estimator, besides hitting the confidence interval around the true value, has the j smallest confidence interval for that distribution and that sizes.

The quality of this Monte Carlo study, when measured by the Mean Standard Deviations (Table 1), is reasonably good. Tables 2 and 3 suggest that this study could be continued in order to determine the asymptotic behaviour of the estimators; this could be the goal of a forthcoming study.

Within the considered size ranges and situations (the experimenter does not know, a priori, if the data come from the pure or contaminated distribution, henceforth all the situations must be considereded globally), the best estimator is the TML. Also, a very poor performance of the MAD estimator has been detected suggesting, thus, not to use it in these situations.

   table787
Table 4: Does the estimator hit the true value?

Table 5 presents the regression coefficients for the models already introduced in equation (6). Notice that, in every regression, ten points are considered; this is not enough to make a detailed regression analysis, but we include these results just to illustrate this important part of every simulation study in Statistics. Forward Regression was used, with the F-to-include and F-to-remove values set to 4. All the regressions discarded the use of explanatory variables; i. e. all the tex2html_wrap_inline2030 , for tex2html_wrap_inline2032 were set to zero and the corresponding explanatory variable ( tex2html_wrap_inline2034 ) excluded from the model. A residual analysis was performed for every regression (10 models), showing no significant structures and, thus, validating the results.

   table835
Table 5: Regressions coefficients.


next up previous
Next: Computational Information Up: An example Previous: The results

Alejandro C. Frery: frery@di.ufpe.br