Abstract:

Balanced ranked set sampling (RSS) is suitable for statistical inference when the population distribution is completely unknown, but if some information about the population distribution is available, the efficiency of statistical inference can be further improved by using certain criteria. Under the criterion of minimum mean square error (MSE), existing literature has found the 3×3 optimal RSS designs for the normal distribution, uniform distribution, and exponential distribution. This paper presents the MSE of estimation of population mean under 4×4 RSS designs and its 35 designs. Based on the criterion of minimum MSE, general conclusions for finding the 4×4 optimal RSS design is given. To improve the accuracy of estimation, the MSE of estimation of population mean under the cyclic 4×4 optimal RSS design is further studied. For the normal distribution, uniform distribution, and exponential distribution, the 4×4 optimal RSS designs under the criterion of minimum MSE are derived. By further studying the MSE of estimation of population mean under the cyclic 4×4 optimal RSS design for these distributions, the research results show that the MSE of estimation of population mean for these distributions under the cyclic 4×4 optimal RSS design continuously decreases with the increase of cycles.

Key words: ranked set sampling, mean squared error, optimal ranked set sampling design