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On Some Smooth Estimators of the Quantile Function for a Stationary Associated Process

Yogendra P. Chaubey (), Isha Dewan () and Jun Li ()
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Yogendra P. Chaubey: Concordia University
Isha Dewan: Indian Statistical Institute, Delhi Centre
Jun Li: Nanjing Audit University

Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 7, 114-139

Abstract: Abstract Let {Xn, n ≥ 1} be a sequence of stationary non-negative associated random variables with common marginal distribution function F(x) and quantile function Q(u), where Q(u) is defined as F(Q(u)) = u. Here we consider the smooth estimation of Q(u), adapted from generalized kernel smoothing (Cheng and Parzen J. Stat. Plann. Infer. 59, 291–307, 1997) of the empirical quantile function. Some asymptotic properties of the kernel quantile estimator, for associated sequences, are also established parallel to those in the i.i.d. case. 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 Chaubey et al. (Statist. Probab. Lett. 81, 267–276, 2011). 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.

Keywords: Associated sequence; Quantile function; Kernel smoothing; Primary 62G07; 62G20; Secondary 62P99 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13571-020-00242-x

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