Evaluation of semivariance estimators under normal conditions

Abstract

When outliers are present in data, the classical estimator of the data's spatial dependence as measured by the semivariogram becomes inefficient and robust estimators are often recommended as being relatively efficient. This study evaluated robust estimator efficiency and bias with normally distributed data to determine how the robust estimator, which is derived using normality arguments, fared. It was conducted by comparing the variances and biases of classical and robust estimates calculated from simulated data for a range of forms of underlying spatial dependences. As the lag distance increases, the robust estimator is found to have an increasingly larger variance than the classical estimator, and, up to the range of the spatial dependence, is increasingly negatively biased. The biases and variances are generally larger when the spatial dependence is strong and become appreciably large when it is far ranging. The results have implications concerning the robust estimator's use with contaminated data. They also indicate that, unless the spatial dependence is neither strong nor far reaching, the disadvantages of using the robust instead of the classical estimator with normally distributed data are severe. This might happen if the user mistakenly suspects that the data contain outliers and, being aware of the instability of the classical estimator in this case, chooses the robust estimator as being the conservative option that its name implies.