A Design Unbiased Variance Estimator of the Systematic Sample Means
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 3, May 2015, Pages: 201-210
Received: May 11, 2015; Accepted: May 18, 2015; Published: May 30, 2015
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Authors
Festus A. Were, Jomo Kenyatta University of Agriculture and Technology, School of Mathematical Sciences, Nairobi, Kenya
George Orwa, Jomo Kenyatta University of Agriculture and Technology, School of Mathematical Sciences, Nairobi, Kenya
Romanus Odhiambo, Jomo Kenyatta University of Agriculture and Technology, School of Mathematical Sciences, Nairobi, Kenya
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Abstract
Systematic sampling is normally used in surveys of finite populations because of its appealing simplicity and efficiency. When properly applied, it can reflect stratification in the population and thus can be more precise than SRS. In systematic sampling technique, the sampling units are evenly spread over the whole population. This sampling scheme is very sensitive to correlation between units in the entire population. A positive autocorrelation reduces the precision while a negative autocorrelation will improve the precision compared to simple random sampling. The limitation of this sampling method is that, it is not possible to estimate the design variance that is unbiased. This study proposes an estimator for the design variance based on a non-parametric model for the population using local polynomial regression as the estimation technique. The non-parametric model is more flexible that it can hold for many practical situations. A simulation study is performed to enable the comparison of the efficiency of the proposed estimator to the existing ones. The performance measures used include: Relative Bias (RB) and Mean Square Error (MSE). From the simulation results, it can be seen that local polynomial estimator based on nonparametric model is consistent and design unbiased for the variance of systematic sample mean. The simulation study gave smaller values for the relative biases and mean squared errors for proposed estimator.
Keywords
Systematic Sampling, Local Polynomial Regression, Non-Parametric Model, Design Variance
To cite this article
Festus A. Were, George Orwa, Romanus Odhiambo, A Design Unbiased Variance Estimator of the Systematic Sample Means, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 3, 2015, pp. 201-210. doi: 10.11648/j.ajtas.20150403.27
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