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A Note on Estimating Variance of Finite Population Distribution Function

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  • Sumanta Adhya
  • Banerjee, Tathagata
  • Chattopadhyay, Gouranga

Abstract

Estimating finite population distribution function is an important problem to the survey samplers since it summarizes almost all the relevant information of interest about the finite population. Moreover due to its nonlinearity estimation of variance of estimators of distribution function remains an active area of research since Chambers et al., 1992. Both analytic and resampling-based variance estimators are developed earlier. Here we poropse a bootstrap hybrid variance estimator of model-based semi-patametric estimator of finite population distribution function estimator. We prove its consistency and also show that its numerical performances are superior to analytical estimator.

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  • Sumanta Adhya & Banerjee, Tathagata & Chattopadhyay, Gouranga, 2015. "A Note on Estimating Variance of Finite Population Distribution Function," IIMA Working Papers WP2015-08-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    • Handle: RePEc:iim:iimawp:13715
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    References listed on IDEAS

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    1. Camelia Goga & Anne Ruiz-Gazen, 2014. "Efficient estimation of non-linear finite population parameters by using non-parametrics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 113-140, January.
    2. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
    3. Sumanta Adhya & Tathagata Banerjee & Gaurangadeb Chattopadhyay, 2011. "Inference on Polychotomous Responses in Finite Populations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(4), pages 788-800, December.
    4. Sumanta Adhya & Tathagata Banerjee & Gaurangadeb Chattopadhyay, 2012. "Inference on finite population categorical response: nonparametric regression-based predictive approach," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(1), pages 69-98, January.
    5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    6. F. J. Breidt & G. Claeskens & J. D. Opsomer, 2005. "Model-assisted estimation for complex surveys using penalised splines," Biometrika, Biometrika Trust, vol. 92(4), pages 831-846, December.
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