A short note on quantile and expectile estimation in unequal probability samples
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by Linda Schulze Waltrup and Göran KauermannNote 1
- Release date: June 22, 2016
The estimation of quantiles is an important topic not only in the regression framework, but also in sampling theory. A natural alternative or addition to quantiles are expectiles. Expectiles as a generalization of the mean have become popular during the last years as they not only give a more detailed picture of the data than the ordinary mean, but also can serve as a basis to calculate quantiles by using their close relationship. We show, how to estimate expectiles under sampling with unequal probabilities and how expectiles can be used to estimate the distribution function. The resulting fitted distribution function estimator can be inverted leading to quantile estimates. We run a simulation study to investigate and compare the efficiency of the expectile based estimator.
Key Words: Quantiles; Expectiles; Probability proportional to size; Design-based; Auxiliary variable; Distribution function.
Table of content
- 1. Introduction
- 2. Quantile estimation
- 3. Expectile estimation
- 4. From expectiles to the distribution function
- 5. Simulations
- 6. Discussion