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.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 4, Issue 3) |
| DOI | 10.11648/j.ajtas.20150403.27 |
| Page(s) | 201-210 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2015. Published by Science Publishing Group |
Systematic Sampling, Local Polynomial Regression, Non-Parametric Model, Design Variance
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APA Style
Festus A. Were, George Orwa, Romanus Odhiambo. (2015). A Design Unbiased Variance Estimator of the Systematic Sample Means. American Journal of Theoretical and Applied Statistics, 4(3), 201-210. https://doi.org/10.11648/j.ajtas.20150403.27
ACS Style
Festus A. Were; George Orwa; Romanus Odhiambo. A Design Unbiased Variance Estimator of the Systematic Sample Means. Am. J. Theor. Appl. Stat. 2015, 4(3), 201-210. doi: 10.11648/j.ajtas.20150403.27
AMA Style
Festus A. Were, George Orwa, Romanus Odhiambo. A Design Unbiased Variance Estimator of the Systematic Sample Means. Am J Theor Appl Stat. 2015;4(3):201-210. doi: 10.11648/j.ajtas.20150403.27
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Download@article{10.11648/j.ajtas.20150403.27,
author = {Festus A. Were and George Orwa and Romanus Odhiambo},
title = {A Design Unbiased Variance Estimator of the Systematic Sample Means},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {4},
number = {3},
pages = {201-210},
doi = {10.11648/j.ajtas.20150403.27},
url = {https://doi.org/10.11648/j.ajtas.20150403.27},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150403.27},
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.},
year = {2015}
}
TY - JOUR T1 - A Design Unbiased Variance Estimator of the Systematic Sample Means AU - Festus A. Were AU - George Orwa AU - Romanus Odhiambo Y1 - 2015/05/30 PY - 2015 N1 - https://doi.org/10.11648/j.ajtas.20150403.27 DO - 10.11648/j.ajtas.20150403.27 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 201 EP - 210 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20150403.27 AB - 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. VL - 4 IS - 3 ER -
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