M. Conde Amboage, C. A. Sánchez Sellero
It is perfectly natural that the precision of quantile estimates should depend on the inverse of the density evaluated at the quantile, called sparsity function, because it reflects the density of observations near the quantile of interest. If the data are very sparse at the quantile of interest, this quantile will be difficult to estimate, but when the density is high, the quantile is more precisely estimated.
Moreover, the asymptotic distribution associated with the parametric quantile regression estimator also depends on the inverse of the conditional density function evaluated at the quantile of interest. In the regression context, this function plays an analogous role to the variance of the errors in least squares estimation of classical mean regression.
Along this talk a new nonparametric estimator of the conditional sparsity function, based on kernel ideas, will be presented. Furthermore, different bandwidth selectors will be compared using a Monte Carlo simulation study.
Keywords: quantile regression, nonparametric estimation, sparsity function.
Scheduled
GT09. NOPAR3
November 9, 2023 11:40 AM
HC1: Canónigos Room 1