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

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  • Chaubey, Yogendra P.
  • Dewan, Isha
  • Li, Jun

Abstract

Let {Xn,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).

Suggested Citation

  • Chaubey, Yogendra P. & Dewan, Isha & Li, Jun, 2011. "Smooth estimation of survival and density functions for a stationary associated process using Poisson weights," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 267-276, February.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:2:p:267-276
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    References listed on IDEAS

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    1. Bagai, Isha & Prakasa Rao, B. L. S., 1991. "Estimation of the survival function for stationary associated processes," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 385-391, November.
    2. Karunamuni, R.J. & Zhang, S., 2008. "Some improvements on a boundary corrected kernel density estimator," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 499-507, April.
    3. W. Gawronski & U. Stadtmüller, 1981. "Smoothing histograms by means of lattice-and continuous distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 28(1), pages 155-164, December.
    4. Chaubey Yogendra P. & Sen Pranab K., 1996. "On Smooth Estimation Of Survival And Density Functions," Statistics & Risk Modeling, De Gruyter, vol. 14(1), pages 1-22, January.
    5. U. Stadtmüller, 1983. "Asymptotic distributions of smoothed histograms," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 30(1), pages 145-158, December.
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    Cited by:

    1. Christophe Chesneau & Isha Dewan & Hassan Doosti, 2012. "Wavelet linear density estimation for associated stratified size-biased sample," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 429-445.
    2. Zohra Guessoum & Abdelkader Tatachak, 2020. "Asymptotic Results for Truncated-censored and Associated Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 142-164, May.
    3. Yogendra P. Chaubey & Isha Dewan & Jun Li, 2021. "On Some Smooth Estimators of the Quantile Function for a Stationary Associated Process," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 114-139, May.

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