Spatial Analyses of Electricity Supply and Consumption in Turkey for Effective Energy Management and Policy-making - Implementing Environmental and Resource Management - page 161

nel Density Estimation, quadrat analysis can be used. With this method, the study
area is divided into certain sized quadrats and the number of events (i.e., the
amount of electricity consumption, the number of power plants) in each quadrat is
mapped. However, in this approach it can be difficult to define an appropriate
quadrat size. For the second order analysis, the Local Moran's I, which was devel-
oped by Luc Anselin (subsection 14.4.2), and Hotspot Analysis (Getis-Ord Gi*
statistics) (subsection 14.4.3) are used to provide local scale correlations. The sec-
ond order effects can also be explored by the Moran's I and Geary's C correlation
measures. These measures provide the spatial correlation throughout the whole
study area. Unfortunately, this is inappropriate for a country scale because it does
not reflect local spatial correlations. For this reason, local spatial correlation
measures were selected as the second order exploration methods.

14.4.1 Kernel Density Estimation

The Kernel Density Estimation (KDE) method has received considerable attention
in the field of nonparametric estimation of probability densities (Wu and Mielnic-
zuk 2002) and is a popular technique for analysing one- and two-dimensional data
(see Scott 1992 and Simono 1996 for examples). There are two types of KDE
functions: fixed and adaptive kernels. The fixed kernel function is usually less
computationally intensive and uses an optimal spatial kernel (bandwidth) over the
study space. Nevertheless, in sparse data seen areas fixed kernel function can pro-
duce large local estimation variance. Contrary to this, if data are dense then it may
mask subtle local variations (Fotheringham et al. 2002; Páez et al. 2002a,b given
in Luo and Wei 2009, p. 57). On the other hand, the adaptive kernel function
represents the spatial heterogeneity degree better than fixed kernel and it ensures
certain number of nearest neighbours as local samples (Luo and Wei 2009, p. 57).
In this study, the adaptive kernel function was used. The general form of KDE is
shown in equation (14.1) and is performed using the Spatial Analyst Tool in
ArcMap 9.3.

n

1 ⎛ − s s ⎞

= ∑ = ()

ˆ

i

λ τ s k (14.1)

⎜ ⎝ ⎟ ⎠

2

τ

τ

i 1

where k ( ) is the kernel,τis the bandwidth, and the adaptive bandwidth is taken as:

α

ˆ

⎛ ⎞

λ

()

⎜
⎝

g

⎟
⎠

τ s = τ (14.2)

()

i 0

⎜ ⎟

τ s

i

ˆ

where 0 ≤ α is the sensitivity parameter, and ≤ 1 is the geometric mean of the

pilot estimates () ˆ

at each

s . i