Determining the Unbiased Estimator of the Population Geometric Measures of Variation about the Mean

Geometric Measures of Variation about the mean is a measure that uses the geometric averaging technique to average the deviations from the mean. From previous studies, it has been determined that the measure is more precise in estimating the average variation about the mean than the existing measures of variation about the mean. Given that the technique is a newly introduced technique of estimating the average variation about the mean, the actual sample estimator for the measure is still unknown, as a result, the study aimed at determining the unbiased estimator for the population geometric measure. The study used a mathematical estimation technique to determine the unbiased estimator among the existing possible estimators as it assumed a simple random sampling without replacement technique. The study determined that the unbiased estimator of the population estimator was the sample estimator which did not allow one degree of freedom.

均值几何变异度量（Geometric Measures of Variation about the Mean）是一类采用几何平均法对均值离差进行平均计算的统计指标。既往研究证实，相较于现有均值变异度量方法，该指标在估计均值平均变异程度时具有更高的精度。由于该技术是新近提出的均值平均变异程度估计方法，其对应的实际样本估计量仍未明确，因此本研究旨在推导该总体几何变异度量的无偏估计量（unbiased estimator）。本研究采用数学估计方法，在现有候选估计量中筛选最优无偏估计量，研究假设采用无放回简单随机抽样（simple random sampling without replacement）方法。最终本研究确定，该总体几何变异度量的无偏估计量为需舍弃1个自由度的样本估计量。