Abstract
In this article, we study the limiting distributions of sample quantiles from a finite population. We give a simple proof of the asymptotic normality of sample quantiles for simple random samples from a finite population by employing the method of Wretman (1978). Some Monte Carlo simulation results are also included.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Blesseos, N.P. (1976). Distribution-Free Confidence Intervals for Quantiles in Stratified and Cluster Sampling Ph.D. Thesis, Illinois Institute of Technology.
Chatterjee, A. (2011). Asymptotic Properties of Sample Quantiles from a Finite Population. Annals of the Institute of Statistical Mathematics 63 157–179.
Cochran, W.G. (1977). Sampling Techniques, 3rd. ed. John Wiley & Sons.
Erdos, P. & A. Renyi (1959). On the Central Limit Theorem for Samples from a Finite Population. Publications of the Mathematical Institute of the Hungarian Academy of Sciences 4, 49–61.
Eeden, van C. & J.Th. Runnenburg (1960). Conditional Limit-distributions for the Entries in a 2 × 2-table, Statistica Neerlandica 14, 111–126.
Francisco, C.A. & W.A. Fuller (1992). Quantile Estimation with a Complex Survey Design. The Annals of Statistics 19, 454–464.
H’ajek, J. (1960). Limiting Distributions in Simple Random Sampling from a Finite Population. Publications of the Mathematical Institute of the Hungarian Academy of Sciences 5, 361–374.
Motoyama, M. & H. Takahashi (2008). Smoothed Versions of Statistical Functionals from a Finite Population. Journal of the Japan Statistical Society 38, 475–504.
Rao, C.R. (1973). Linear Statistical Inference and Its Applications, 2nd. ed. John Wiley & Sons.
Rosen, B. (1964). Limit Theorems for Sampling from Finite Populations, Arkiv for Matematik 5, 383–424.
Sedransk, J. & J. Meyer (1978). Confidence Intervals for the Quantiles of a Finite Population: Simple Random and Stratified Simple Random Sampling. Jounal of the Royal Statistical Society. Series B(Methodological) 40, 239–252.
Sedransk, J. & P.J. Smith (1988). Inference for Finite Population Quantiles, in P.R. Krishnaiah and C.R. Rao, eds., Handbook of Statistics, Vol. 6 Elsevier Science Publishers B.V., 267–289.
Shao, J. (1994). L-Statistics in Complex Survey Problem. The Annals of Statistics 22, 946–967.
Siddiqui, M.M. (1960). Distribution of Quantiles in Samples from a Bivariate Population. Journal of Research of the National Bureau of Standards-B. Mathematics and Mathematical Physics 64B, 145–150.
van der Vaart, H.R. (1961). A Simple Derivation of the Limiting Distribution Function of a Sample Quantile with Increasing Sample Size. Statistica Neerlandica 5, 239–242.
Walker, A.M. (1968). A Note on the Asymptotic Distribution of Sample Quantiles. Journal of the Royal Statistical Society. Series B (Methodological) 30, 570–575.
Wilks, S.S. (1962). Mathematical Statistics John Wiley & Sons.
Wretman, J. (1978). A Simple Derivation of the Asymptotic Dstribution of a Sample Quantile. Scandinavian Journal of Statistics 5, 123–124.
Author information
Authors and Affiliations
Additional information
This research was partially supported by Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology 21730172 and 21330048.
About this article
Cite this article
Motoyama, H. Note on a Simple Derivation of the Asymptotic Normality of Sample Quantiles from a Finite Population. Behaviormetrika 39, 1–8 (2012). https://doi.org/10.2333/bhmk.39.1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.2333/bhmk.39.1