Linear Systematic Sampling

Linear systematic sampling design is very simple and operationally convenient in practice, but, when the population size is not a multiple of the sample size, results in a variable sample size and in this case sample mean as an estimator of the population mean is not unbiased. To overcome these difficulties and in some cases to increase the efficiency, a number of modifications of linear systematic sampling design have been proposed, such as centered systematic sampling, balanced systematic sampling and modified systematic sampling etc.. In particular, Mahalanobis (1946), Deming (1950), Gautschi (1957) and Shiue (1960) considered a multiple-start systematic sampling scheme; Murthy and Rao (1988) discussed the circular systematic sampling method. Singh and Padam Singh (1977) proposed a method termed new systematic sampling; Padam Singh and Garg (1979) suggested a balanced random sampling design; Leu and Tsui (1996) considered a new partially systematic sampling. Note that all of the modified designs above provided a fixed sample size and an unbiased estimator of the population mean. In the present study, a new sampling scheme called remainder linear systematic sampling is established to extend the linear systematic sampling for the case in which population size is not a multiple of sample size. The efficiency of the proposed procedure has been compared with simple random sampling and in some cases, circular systematic sampling and new partially systematic sampling for various types of populations.