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Wavelet linear density estimation for associated stratified size-biased sample

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  • Christophe Chesneau
  • Isha Dewan
  • Hassan Doosti

Abstract

Ramirez and Vidakovic [(2010), ‘Wavelet Density Estimation for Stratified Size-Biased Sample’, Journal of Statistical Planning and Inference, 140, 419–432] considered an estimator of the density function based on wavelets with independent stratified random variables from weighted distributions. They proved that it is L2-consistent. In this paper, we complete this result by determining the rate of convergence attained by a slightly modified version of their estimator (including an estimator of the normalisation parameters). Then, we explore the case when the random variables are negatively and positively associated within strata. The theory is illustrated with a simulation study.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:429-445
    DOI: 10.1080/10485252.2012.672024
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    References listed on IDEAS

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    1. Masry, Elias, 1994. "Probability density estimation from dependent observations using wavelets orthonormal bases," Statistics & Probability Letters, Elsevier, vol. 21(3), pages 181-194, October.
    2. Shen, Yu & Ning, Jing & Qin, Jing, 2009. "Analyzing Length-Biased Data With Semiparametric Transformation and Accelerated Failure Time Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1192-1202.
    3. 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.
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    Cited by:

    1. Aleksandr Beknazaryan & Hailin Sang & Peter Adamic, 2023. "On the integrated mean squared error of wavelet density estimation for linear processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 235-254, July.
    2. Renyu Ye & Xinsheng Liu & Yuncai Yu, 2020. "Pointwise Optimality of Wavelet Density Estimation for Negatively Associated Biased Sample," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    3. Chesneau, Christophe & Dewan, Isha & Doosti, Hassan, 2016. "Nonparametric estimation of a quantile density function by wavelet methods," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 161-174.
    4. Youming Liu & Junlian Xu, 2014. "Wavelet density estimation for negatively associated stratified size-biased sample," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 537-554, September.

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