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On Some Aspects of Rank Set Sampling and Non-Response Situations Utilizing R/SAS Softwares

KrishiKosh

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Title On Some Aspects of Rank Set Sampling and Non-Response Situations Utilizing R/SAS Softwares
 
Creator Bhat, M Iqbal Jeelani
 
Contributor Mir, S.A.
 
Subject Rank set sampling, Ratio estimators, Proposed ratio estimators, Non-Response, Allocations, SAS, R-software
Agricultural Statistics
 
Description PhD Thesis submitted SKUAST K
The present study was carried out on Rank set sampling with a view of increasing the efficiency of estimate of population mean. The basic premise for ranked set sampling (RSS) is an infinite population under study and the assumption that a set of sampling units drawn from the population can be ranked by certain means rather cheaply without the actual measurement of the variable of interest which might be costly and/or time-consuming. The essence of RSS is similar to the classical stratified sampling. RSS can be considered as post-stratifying the sampling units according to their ranks in a sample. In present study simple linear regression models were considered with respect to samples taken from the identified sampling techniques like simple random sampling (SRS), systematic sampling (SYS) and rank set sampling (RSS). It was found that the coefficient of determination obtained from regression model based on rank set sample was higher than rest of two sampling schemes. Root mean square error, p values, coefficient of variation were much lower in rank set based regression model than others. Kernel density curves were more symmetric in case of rank set sample as compared to SRS and SYS. Using validation technique (Jacknifing) there was consistency in the measure of R2, Adj R2 and RMSE in case of RSS as compared to SRS and SYS. Ranked set sampling is introduced within the frame work of stratified sampling. Rather than selecting a simple random sample within each stratum as is done in stratified simple random sampling (SSRS), a ranked set sample within each stratum is taken. From the simulation results it is concluded that RSS, when used in place of SRS in the final stage of stratified sampling, can provide considerably more accurate estimates of population means. New ratio estimators for RSS are proposed based on various combinations of known values of deciles, Median, Quartile deviation, coefficient of Skewness, Kurtosis, and Correlation coefficient of auxiliary variable. The proposed ratio estimators were more efficient than classical ratio estimators, and from various simulation results it was found that the efficiency of RSS estimators decreases as the correlation coefficient decreases, the efficiency increases as the set size m increases. Population mean under non responses is also studied under rank set sampling. Some new allocation schemes were proposed under RSS in order to study their effect on sampling variance. In most of the situations under different combinations of non-response rate and inverse ratio of sub-sampled non-response class, allocation schemes depending solely upon the knowledge of stratum size, non-response rate, mean squares of non-response group produces more precise estimates as compared to proportional allocation and other allocations based on knowledge of response and non-response rate only. From the results it is concluded that in addition to the knowledge of strata sizes, the knowledge of non-response rates and mean squares among non-response groups while allocating sample to different strata, improves the precision of the estimate. Different computer programmes were prepared using R-software and the analysis as per the objectives were carried out. In the preliminary study regression analysis and regression diagnostics was carriedout in SAS, while the simulation was carried out using the function library (mvtnorm) in R software. With the help of R -software new functions like drss(m,r), varwts(n,h), makeAlloc (n,m)and ratio.est(n,N(x,y))were developed. All these functions were run on real data set generated from forestry and horticultural crops.
SKUAST K
 
Date 2016-12-21T13:11:49Z
2016-12-21T13:11:49Z
2014
 
Type Thesis
 
Identifier http://krishikosh.egranth.ac.in/handle/1/91788
 
Language en
 
Format application/pdf