Abstract
The aim of the paper is to establish asymptotics in sampling finite populations. Asymptotic results are first established for an analogous of the empirical process based on the Hájek estimator of the population distribution function and then extended to Hadamard-differentiable functions. As an application, asymptotic normality of estimated quantiles is provided.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Berger, Y.G.: Rate of convergence to normal distribution for the Horvitz–Thompson estimator. J. Stat. Plan. Inference 67, 209–226 (1998)
Chatterjee, A.: Asymptotic properties of sample quantiles from a finite population. Ann. Inst. Stat. Math. 63, 157–179 (2011)
Chen, J., Wu, C.: Estimation of distribution function and quantiles using the model-calibrated pseudo empirical likelihood method. Stat. Sin. 12, 1223–1239 (2002)
Conti, P.L.: On the estimation of the distribution function of a finite population under high entropy sampling designs, with applications. Sankhya 76-B, 234–259 (2014)
Csörgő, M.: Quantile Processes with Statistical Applications. SIAM, Philadelphia (1983)
Csörgő, M., Csörgő, S., Horváth, L.: An Asymptotic Theory for Empirical Reliability and Concentration Processes. Springer, Berlin (1986)
Francisco, C.A., Fuller, W.A.: Quantile estimation with a complex survey design. Ann. Stat. 19, 454–469 (1991)
Hájek, J.: Asymptotic theory of rejective sampling With varying probabilities from a finite population. Ann. Math. Stat. 35, 1491–1523 (1964)
Kuk, A.Y.C.: Estimation of distribution functions and medians under sampling with unequal probabilities. Biometrika 75, 97–103 (1988)
Rao, J.N.K., Kovar, J.G., Mantel, J.G.: On estimating distribution functions and quantiles from survey data using auxiliary information. Biometrika 77, 365–375 (1990)
Rueda M., Martinez, S., Martinez, H., Arcos, A.: Estimation of the distribution function with calibration methods. J. Stat. Plan. Inference 137, 435–448 (2007)
Sedransk, J., Meyer,J.: Confidence intervals for the quantiles of a finite population: simple random and stratified random sampling. J. R. Stat. Soc. B 40, 239–252 (1978)
Sedransk, J., Smith, P.: Lower bounds for confidence coefficients for confidence intervals for finite population quantiles. Comput. Stat. Theory Methods 12, 1329–1344 (1983)
Serfling, R.J.: Approximation Theorems of Mathematical Statistics. Wiley, New York (1980)
Shao, J.: L-statistics in complex survey problems. Ann. Stat. 22, 946–967 (1994)
Sitter, R.R., Wu, C.: A note on Woodruff confidence intervals for quantiles. Stat. Probab. Lett. 52, 353–358 (2001)
Tillé, Y.: Sampling Algorithms. Springer, New York (2006)
Van Der Vaart, A.: Asymptotic Statistics. Cambridge University Press, Cambridge (1998)
Víšek, J A.: Asymptotic distribution of simple estimate for rejective, Sampford and successive sampling. In: Jurec̆ková, J. (ed.) Contributions to Statistics, pp. 263–275. Reidel Publishing Company, Dordrecht (1979)
Woodruff R.S.: Confidence intervals for medians and other position measures. J. Am. Stat. Assoc. 47, 635–646 (1952)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Conti, P.L., Marella, D. (2015). Asymptotics in Survey Sampling for High Entropy Sampling Designs. In: Morlini, I., Minerva, T., Vichi, M. (eds) Advances in Statistical Models for Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-17377-1_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-17377-1_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17376-4
Online ISBN: 978-3-319-17377-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)