Row and Column Elimination Sampling Design +1 and its Efficiencies

Extended Abstract. It is a traditional way in biological, sociological, agricultural and geological studies to partition a geographical area into quadrats and then take a sample of them by a particular sampling design. We study the relevant characteristic of quadrats to estimate a parameter of the population. We suppose that the variable of interest has a positive spatial autocorrelation. Sampling designs which produce an appropriate coverage of the population will increase the precision of the parameter estimator, (Schreuder et al, 1993). Hájek (1959), under a model with a positive spatial autocorrelation, illustrated that the systematic sampling is an optimum sampling design for one dimensional population. However, systematic and stratified samplings with only one sample in each stratum, are two traditional sampling designs that cover the population region well (McKenzie et al, 1991). Unfortunately, there is no unbiased estimator for these two sampling designs. Simple Latin Square Sampling (SLSS) design is another design which provides a good coverage for population. Also, this design has no variance estimator and it is considered as a weak point in practice. Munholland and Borkowski, (1995) introduced Simple Latin Square Sampling +1 (SLSS+1). They suggest that taking one additional sampling unit helps to provide an unbiased variance estimator. However, two other problems still exist concerning SLSS and SLSS+1. The population has to be a square and also the sample size be restricted to square root of the population size. Salehi (2002) introduced Systematic Simple Latin Square Sampling (SSLSS) for...[To continue please click here]