On some smooth estimators of the quantile function for a stationary associated process
The authors aimed to quantile function estimation to estimating marginal distribution function. Various estimators in this class of estimators are contrasted, through a simulation study, among themselves and with an indirect smooth quantile estimator obtained by inverting the Poisson weights based estimator of the distribution function studied in [\textit{Y. P. Chaubey} et al., Stat. Probab. Lett. 81, No. 2, 267--276 (2011; Zbl 1270.62067)]. The indirect smoothing estimator seems to be the best estimator on account of smaller MSE, however, a quantile estimator based on the Bernstein polynomials and that using the corrected Poisson weights turn out to be almost as good as the inverse distribution function estimator using Poisson weights. As far as my knowledge goes, the author's statistical approach fulfills the standards of the journal. The abstract is succinct and appropriate and reflecting the essence of the paper. The methodology used is clear and utmost care is taken about typographical errors. It seems that the authors explained an important conclusion based on the numerical studies is that the quantile estimator obtained by inverting the smooth estimator of the distribution function using Poisson weights comes out to be the best amongst the considered estimators. On the other hand, the direct smooth estimators using the normalized Poisson weights and Bernstein polynomials are good competitors. The authors explained through theoretically.
scientific article; zbMATH DE number 7383744
scientific article