Abstract
In this paper we investigate the Fisher information matrix of a rounded ranked set sampling (RSS) sample and show that the sample is always more informative than a rounded simple random sampling (SRS) sample of the same size. On the other hand, we propose a new method to approximate maximum likelihood estimates (MLE) of unknown parameters for this model and further establish the strong consistency and asymptotic normality of the proposed estimators. Simulation experiments show that the approximated MLE based on rounded RSS is always more efficient than those based on rounded SRS.
Similar content being viewed by others
References
Bai ZD, Zheng SR, Zhang BX, Hu GR (2009) Statistical analysis for rounded data. J Stat Plan Inference 139: 2526–2542
Chen ZH (2000) The efficiency of ranked set-sampling relative to simple random sampling under multi-parameter families. Statistica Sinica 10: 247–263
Chen ZH, Bai ZD, Sinha BK (2003) Ranked set sampling: theory and applications. Springer
Coppejans M (2003) Effective nonparametric estimation in the case of severely discretized data. J Econom 117: 331–367
Dell TR, Clutter JL (1972) Ranked set sampling theory with order statistics background. Biometrics 28: 545–555
Dempster AP, Rubin DB (1983) Rounding error in regression: the appropriateness of sheppard’s corrections. J R Stat Soc Ser B 45: 51–59
Heitjan DF, Rubin DB (1991) Ignorability and coarse data. Ann Stat 19: 2244–2253
Lee CS, Vardeman SB (2001) Interval estimation of a normal process mean from rounded data. J Qual Technol 33: 335–348
Lee CS, Vardeman SB (2002) Interval estimation of a normal process standard deviation from rounded data. Commun Stat Simul Comput 31: 13–34
Lee CS, Vardeman SB (2003) Confidence interval based on rounded data from the balanced one-way normal random effects model. Commun Stat Simul Comput 32: 835–856
McIntyre GA (1952) A method for unbiased selective sampling, using ranked sets. Aust J Agric Res 3: 385–390
Sheppard WF (1898) On the calculation of the most probable values of frequency constants, for data arranged according to equidistant divisions of a scale. Proc London Math Soc 29: 353–380
Stokes SL (1980) Estimation of variance using judgment ordered ranked-set samples. Biometrics 36: 35–42
Takahasi K, Wakimoto K (1968) On unbiased estimates of the population mean based on the sample stratified by means of ordering. Ann Inst Stat Math 20: 1–31
Tricker AR (1990) The effect of rounding on the significance level of certain normal test statistics. J Appl Stat 17: 31–38
Tricker A, Coates E, Okell E (1998) The effect on the r chart of precision of measurement. J Qual Technol 30: 232–239
Vardeman SB (2005) Sheppard’s correction for variances and the quantization noise model. IEEE Trans Instrum Meas 54: 2117–2119
Vardeman SB, Lee CS (2005) Likelihood-based statistical estimation from quantization data. IEEE Trans Instrum Meas 54: 409–414
Zhang BX, Liu TQ, Bai ZD (2009) Analysis of rounded data from dependent sequences. Ann Inst Stat Math. doi:10.1007/s10463-009-0224-6
Author information
Authors and Affiliations
Corresponding author
Additional information
The work of the third author was partially supported by the NSF China grant 10871036.
Rights and permissions
About this article
Cite this article
Li, W., Liu, T. & Bai, Z. Rounded data analysis based on ranked set sample. Stat Papers 53, 439–455 (2012). https://doi.org/10.1007/s00362-010-0351-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-010-0351-4