A short note on quantile and expectile estimation in unequal probability samples 6. Discussion
In Section 4 we extended the toolbox of expectiles to the estimation of distribution functions in the framework of unequal probability sampling. We defined expectiles for unequal probability samples. When comparing quantiles based on with quantiles based on the expectile based estimator we observed that the proposed estimator performs well in comparison to existing methods. The calculation of empirical expectiles is implemented in the open source software R (see R Core Team 2014) and can be found in the R-package expectreg by Sobotka, Schnabel, and Schulze Waltrup (2013). The calculation of the expectile based distribution function estimator is also part of the R-package expectreg. The calculation of is, however, more demanding as the calculation of because it involves three steps: First, we calculate the weighted expectiles as described in Section 3; second, we estimate and in a third step, we derive from (see Section 4). In the Log-Normal-Simulation it takes about 2-3 seconds for to calculate whereas the computational effort of is barely noticeable.
Both authors acknowledge financial support provided by the Deutsche Forschungsgemeinschaft DFG (KA 1188/7-1).
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