Estimation for Ranked Set Sampling Under Complete and Censored Data
Didem Egemen, Sibel Balci, Baris Surucu
Statistics, Middle East Technical University, Ankara, Turkey

Ranked set sampling is a data collection technique which has been shown to lead to more precise estimators when compared with simple random sampling. The technique was introduced by McIntyre (1952) and numerous works have been done on this subject; see Stokes and Sager (1988), Patil et al. (1994), Ozturk (1999), Yu et al (1999) and Akkaya and Balci (2006). In this work, we consider the parameter estimation and firstly work with complete samples of some distributions. We make use of the modified maximum likelihood (MML) method to estimate unknown parameters. The MML method was introduced by Tiku (1967) and it is known to give very efficient and robust estimators. MML estimators are also asymptotically equivalent to maximum likelihood estimators; see Tiku and Suresh (1992). We compare the efficiencies of the MML estimators with classical estimators obtained from simple random sampling procedure. The distributional properties of MML estimators are also given. A simulation study is also conducted to examine efficiencies.

Many works so far have been done on complete samples. However, a limited number of works has noted the usage of ranked set sampling for censored samples; see for example Yu and Tam (2002). In the second part of the work, we consider several distributions and make use of MML estimation for both type I and type II censored samples. Distributional properties of the MML estimators are examined under these two types of censoring schemes. Moreover, we conduct a simulation study to compare the efficiencies of the MML estimators with those of classical estimators. Real life examples are given to explain the concept.

Bibliography:

Akkaya, A.D. and Balci, S. (2006). Ranked set sampling, BAP-08-11-DPT2002K120510, METU BAP Project Report.

McIntyre, G.A. (1952). A method for unbiased selective sampling using ranked sets. Australian Journal of Agricultural Research, 3, 385-390.

Ozturk, O. (1999). Two sample inference based on one sample ranked set sample sign statistics. J. Nonparametr. Statist., 10, 197-212.

Patil, G.P., Sinha, A.K. & Taillie, C. (1994). Ranked set sampling. Handbook of Statistics, Environmental Statistics, Vol. 12, G.P. Patil & C.R. Rao, eds, North-Holland, Amsterdam.

Stokes, S.L. and Sager, T.W. (1988). Characterization of a ranked-set sample with application to estimating distribution functions. J. Amer. Statist. Assoc., 83, 374-381.

Tiku, M.L. (1967). Estimating the Mean and Standard Deviation from a Censored Normal Sample. Biometrika, 54, 155-165.

Tiku, M.L. and Suresh, R.P. (1992). A new method of estimation for location and scale parameters. J. Stat. Planning and Inference, 30, 281-92.

Yu, P.L.H., Lam, K. & Sinha, B.K. (1999). Estimation of normal variance based on balanced and unbalanced ranked set samples. Environmental and Ecological Statistics, 6, 23 46.

Yu, P.L.H. and Tam, C.Y.C. (2002). Ranked set sampling in the presence of censored data. Environmetrics, 13(4), 379-396.

Keywords: Ranked Set Sampling; Robustness; Modified Maximum Likelihood; Censoring

Biography: Baris Surucu is the Associate Professor of Statistics at the Middle East Technical University, Turkey. He is specialized in distributional theory, goodness-of-fit tests and reliability in the statistics area. Dr. Surucu has published a number of papers on these subjects.