Smooth estimation of survival and density functions for a stationary associated process using Poisson weights

• Published in: Statistics & probability letters 2011-02, Vol.81 (2), p.267-276
• Main Authors: Chaubey, Yogendra P., Dewan, Isha, Li, Jun
• Format: Article
• Language: English
• Subjects: Associated sequence; Associated sequence Hille's theorem Strong consistency Survival function Transformation density estimator; Exact sciences and technology; General topics; Hille’s theorem; Mathematics; Nonparametric inference; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Stochastic processes; Strong consistency; Survival function; Transformation density estimator
• ISSN: 0167-7152; 1879-2103
• DOI: 10.1016/j.spl.2010.10.010

Let { X n , n ≥ 1 } be a sequence of stationary non-negative associated random variables with common marginal density f ( x ) . Here we use the empirical survival function as studied in Bagai and Prakasa Rao (1991) and apply the smoothing technique proposed by Gawronski (1980) (see also Chaubey and Sen, 1996) in proposing a smooth estimator of the density function f and that of the corresponding survival function. Some asymptotic properties of the resulting estimators, similar to those obtained in Chaubey and Sen (1996) for the i.i.d. case, are derived. A simulation study has been carried out to compare the new estimator to the kernel estimator of a density function given in Bagai and Prakasa Rao (1996) and the estimator in Buch-Larsen et al. (2005).