Nonparametric Estimation for Random Censored Data Based on Ranking Set Sampling

In the case where the population distribution is unknown, the Kaplan–Meier estimator of the reliability function based on a ranked set sample with random right-censored data is first proposed. It is shown to be a unique self-consistent estimator. Then, the censored RSS estimator of the population mean is constructed. A simulation study is conducted to compare the performance of the proposed estimators with the corresponding estimators based on a simple random sample. It is shown that the ranked set sampling has higher efficiency. Finally, the proposed method is applied to a renal carcinoma study.

[1]  Omer Ozturk,et al.  Rank Regression in Ranked-Set Samples , 2002 .

[2]  Alessandra Petrucci,et al.  Ranked set sampling allocation models for multiple skewed variables: an application to agricultural data , 2009, Environmental and Ecological Statistics.

[3]  Lirong Cui,et al.  A Further Study on Reliable Life Estimation under Ranked Set Sampling , 2012 .

[4]  Francisco J. Samaniego,et al.  Nonparametric Maximum Likelihood Estimation Based on Ranked Set Samples , 1994 .

[5]  Douglas A. Wolfe.  Ranked set sampling: An approach to more efficient data collection , 2004 .

[6]  Narayanaswamy Balakrishnan,et al.  BLUEs of Parameters of Generalized Geometric Distribution Using Ordered Ranked Set Sampling , 2005 .

[7]  Narayanaswamy Balakrishnan,et al.  Ordered ranked set samples and applications to inference , 2008 .

[8]  T. Sager,et al.  Characterization of a Ranked-Set Sample with Application to Estimating Distribution Functions , 1988 .

[9]  Douglas A. Wolfe,et al.  A new ranked set sample estimator of variance , 2002 .

[10]  S. Lynne Stokes,et al.  Inferences on the Correlation Coefficient in Bivariate Normal Populations from Ranked Set Samples , 1980 .

[11]  Jian Huang.  Asymptotic properties of the NPMLE of a distribution function based on ranked set samples , 1997 .

[12]  P. Royston,et al.  Visualizing length of survival in time-to-event studies: a complement to Kaplan-Meier plots. , 2008, Journal of the National Cancer Institute.

[13]  Chunming Zhang,et al.  Ranked Set Sampling: Theory and Applications , 2005, Technometrics.

[14]  Z. Bai,et al.  Ranked set sampling , 2004 .

[15]  M. Pagano,et al.  Survival analysis. , 1996, Nutrition.

[16]  Lirong Cui,et al.  Optimal sign test for quantiles in ranked set samples , 2010 .

[17]  G. McIntyre,et al.  A method for unbiased selective sampling, using ranked sets , 1952 .

[18]  J. L. Clutter,et al.  Ranked Set Sampling Theory with Order Statistics Background , 1972 .

[19]  Thomas P. Hettmansperger.  The ranked-set sample sign test , 1995 .

[20]  Philip L. H. Yu,et al.  Ranked set sampling in the presence of censored data , 2002 .

[21]  Nicolle A. Mode,et al.  Ranked set sampling for ecological research: accounting for the total costs of sampling , 1999 .

[22]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .