Nonparametric estimation of quantile density function

Nonparametric Estimation of Quantile and Quantile Density Function

“…in the kernel quantile density estimators. The Epanechnikov kernel, which gives the optimal kernel, see Prakasa Rao [34], was studied by Soni [23] for comparing non-parametric quantile density estimators and our simulation showed that Q(u) estimation behaviors under Epanechnikov kernel and triangular kernel were quite close, which was also confirmed in the study of Soni [23]. For simplicity, only the result of the Epanechnikov kernel was presented here.…”

“…These matches with our finding in simulation study that KPL Q and M Q can be away from the true quantile function for large values of u when data is heavily censored. Some techniques for correction at tails have already been explored and a brief review can be found in Soni et al [23]. In addition, as we found in the simulation study, Ĉ q performs the best among all quantile density estimators.…”

“…Epanechnikov kernel function, ( ) ( ) 2 0.75 1 u I u 1 − ≤ , was utilized here for the considered kernel estimators. Note that even though the triangular kernel is more commonly used for kernel quantile estimators in literature, see Padgett [18], Nair and Sankaran [33], and Soni [23], it fails to provide a useful derivative when calculating the K 1 (.) in the kernel quantile density estimators.…”

“…The former way is more advantageous over the latter in terms of efficiency; see Jones [20] for more information pertaining to the comparison of these two methods. In addition, kernel smoothing of the reciprocal of density quantile function has also been considered [23]. As mentioned before, PLQ and EQ estimators fail to provide useful quantile density function estimation.…”

Further theoretical and practical insight to the do-validated bandwidth selector

“…This is indeed being done at the moment, see Gámiz-Pérez et al (2013a,b,c) for the introduction of do-validation to three fundamental models of survival analysis. Do-validation could be considered in other smoothing problems, see for example Soni et al (2012), Oliveira et al (2012), Spreeuw et al (2013), Lee et al (2010Lee et al ( , 2012a, Buch-Kromann and Nielsen (2012), González-Manteiga et al (2013).…”