Some Research On Diagonal Systematic Sampling

The systematic sampling is one of the most basic sampling methods of the sampling survey, and is widely used in the actual survey work. Compared with other sampling methods, systematic sampling has the advantages of simple operation,convenient and economical, and does not require a complete sampling frame. When the population trend is linear, the systematic sampling has a higher precision. Many experts and scholars put forward different methods on how to further improve the accuracy of the systematic sampling. These methods performed well on eliminating the deviation which was caused by different initial unit position in the systematic sampling.The Subramani(2000) proposed the diagonal systematic sampling method is proved to be an effective systematic sampling method. Compared with systematic sampling, the precision of diagonal systematic sampling is obviously improved, but the diagonal systematic sampling methods that Subramani(2000,2010) proposed is only suitable the situation for N ?nk, where k is the sampling interval. when the population size N is not a multiple of the sample size n, the sample mean is biased to the total mean. In order to solve this problem, Chang and Huang(2000) proposed a remainder linear systematic sampling creatively. The remainder linear systematic sampling divided the population into two parts, each part of the overall are integer multiples of the sample size, then estimated the unbiased sample mean. This idea has also been applied to the remainder Markov systematic sampling by Fei-Fei Kao, atc.(2011).In this paper, we extend the the diagnal systematic sampling theory that proposed by Subramani(2000, 2010), and give out the derivation process. Combining the advantages of diagonal systematic sampling and remainder linear systematic sampling, we establish the remainder diagonal systematic sampling theory system, and give the expression of mean and variance. When the population showed a linear trend, the simplified formula is consistent with Subramani(2000-2010)’s. For different situations, the remainder diagonal systematic sampling given their mean and variance expressions. Finally, use the examples to compare remainder diagonal systematic sampling with remainder linear systematic sampling and simple random sampling. The results proved that the efficiency of remainder linear systematic sampling was significantly higher than the other two kinds of methods.In the actual sampling, many resources survey is in the plane regions, such as crop yield investigation, the species abundance survey and so on. In this paper, we arrange the population in a matrix with M rows and N columns, then imply the remainder diagonal systematic sampling methods with the rows and columns separately, and gives the specific sampling procedures and possible samples. When M ?ml, N ?nk, given the estimates’ expression, and calculated the results. It is showed that, remainder diagonalsystematic sampling methods is also performed in the plane population, and the sampling effect is better than the spatial systematic sampling and simple random sampling.