Comparing the Thiessen’s Method against simpler alternatives using Monte Carlo Simulation

Abstract

Estimating the expected value of a function over geographic areas is problem with a long history. In the beginning of the XX-th century the most common method was just the arithmetic mean of the field measurements ignoring data location. In 1911, Thiessen introduced a new weighting procedure measuring influence through an area and thus indirectly considering closeness between them. In another context, Quenouville created in 1949 the jackknife method which is used to estimate the bias and the standard deviation. In 1979 Efron invented the bootstrap method which, among other things, is useful to estimate the expected value and the confidence interval (CI) from a population. Although the Thiessen’s method has been used for more than 100 years, we were unable to find systematic analysis comparing its efficiency against the simple mean, or even to more recent methods like jackknife or boostrap. In this work we compared four methods to estimate de expected value.  Sample mean, Thiessen, the so called here jackknifed Thiessen and bootstrap. All of them are feasible for routine use in a network of fixed locations. The comparison was made using the Friedman’s Test after a Monte Carlo simulation. Two cases were taken for study: one analytic with three arbitrary functions and the other using experimental data from daily rain measured with a satellite. The results show that Thiessen’s method is the best estimator in almost all the cases with a 95% of confidence interval. Unlike the others, the last two considered methods supply a suitable CI, but the one obtained through jackknifed Thiessen was even more accurate, opening the door for future work.