TITLE:
Estimating the Variance of the Proportion of Contaminated Soil by Petroleum Spills Using Two-Dimensional Systematic Sampling under Different Approaches
AUTHORS:
Diego Jarquin
KEYWORDS:
Accurate Estimation of Variance, Model-Assisted Approach, Geary Index, Geostatistics, Oil Spills, Simulation
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.4,
August
23,
2018
ABSTRACT: In
leading petroleum-producing countries like Kuwait, Brazil, Iran, Iraq
and Mexico oil spills frequently occur on land, causing serious damage to crop
fields. Soil remediation requires constant monitoring of the polluted area. One
common monitoring method involves two-dimensional systematic sampling, which
can be used to estimate the proportion of the contaminated soil and study the
oil spills’ geographic distribution. A well-known issue using this sampling
design involves the analytical derivation of variance of the sample mean
(proportion), which requires at least two independent samples. To address the
problem, this research proposed a variance estimator based on regression and a
corrected estimator using the autocorrelation Geary Index under the
model-assisted approach. The construction of the estimators was assisted by
geo-statistical models by simulating an auxiliary variable. Similar populations
to those in real oil spills were recreated, and the accuracy of proposed
estimators was evaluated by comparing their performance with other well-known
estimators. The factors considered in this simulation study were: a) the model
for simulating the populations (exponential and wave), b) the mean and the
variance of the process, c) the level of autocorrelation among units. Given the
statistical and computing burdens (bias, ratio between estimated and real
variance, convergence and computer time), under the exponential model, the
regression estimator showed the best performance; and for the wave model, the
corrected version performed even better.