A short note on quantile and expectile estimation in unequal probability samples
6. DiscussionA 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.
Acknowledgements
Both authors acknowledge financial support provided by the Deutsche
Forschungsgemeinschaft DFG (KA 1188/7-1).
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