It is well known that explicit expression for the Variance of linear systematic sample mean in the presence of linear trend is available in literature. Is there any such explicit expression for the variance of Circular Systematic Sample mean in the presence of linear trend exist?
Dear Dr. Jambulingam Subramani,
I am Fumito Muguruma from Tokyo, JAPAN.
For Circular and Continuous Systematic Sampling, named Roulette Model, I succeeded in calculating an explicit formula for the variance of sample mean. It is written in Theorem 2 of the following paper.
Muguruma, Fumito. "Roulette Model of Systematic Sampling." American Journal of Applied Mathematics and Statistics 2.5 (2014): 344-351.
http://pubs.sciepub.com/ajams/2/5/8/index.html
Please read the paper and ask me any question if you have.
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