Yu, Keming and Jones, M. C.
A comparison of local constant and local linear regression quantile estimators.
Computational Statistics and Data Analysis, 25(2),
Two popular nonparametric conditional quantile estimation methods, local constant fitting and local linear fitting, are compared. We note the relative lack of differences in results between the two approaches. While maintaining the expected preference for the local linear version, the arguments in favour are relatively slight, at least in the interior, and not as compelling as may be thought. The main differences between the approaches lie at the boundaries.
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