Comparison Between Iterative Least Square and Nonparametric Epanechnikov Kernel in Semivariogram Modeling, Case study: Urban Land Cover in East Java Province

Departement of Mathematics, Institut Teknologi Bandung, Bandung, West Java, Indonesia

^* Corresponding author: kurnia@math.itb.ac.id

Abstract

Landcover is an example of spatial data that contains location coordinate information along with the variables measured at each location, namely height, slope, and curvature. The spatial relationship between locations can be measured using a semivariogram. Semivariogram is a statistic used to measure the spatial correlation of pairs of locations separated by a certain distance and angle. In estimating semivariogram parameters, namely, nugget, sill, and range, there are two methods, namely parametric via iterative least squares and nonparametric via kernel functions. These two methods will be compared for semivariogram modeling of built-up land in East Java province. The best method is selected based on the smallest SSE value. For each physical factor, the best model with the smallest SSE is the Epanechnikov kernel function, with 3.6 for the elevation SSE, 8.84 ⋅ 10⁻⁷ for the slope SSE, and 2.15 ⋅ 10⁻²¹ for the curvature SSE. So, it is concluded in this case that the nonparametric kernel Epanechnikov method is much better than the parametric method using Gaussian and exponential models.