Contiguous Unit Based Spatial Sampling technique is a GIS 
based sequential technique for area sampling. It is a draw by draw 
sampling procedure characterised by inclusion probabilities 
varying at each draw. The probability of selection of any unit is 
calculated using the weights obtained from the spatial correlation 
structure and the size measure of auxiliary variable. The method 
is discussed below. 
3.1.1 Estimation of Spatial Correlation and test of Stationarity 
The spatial correlation B for the auxiliary character is estimated 
using the formula given by Moran (1950) and stationarity of 
spatial correlation in order to create zones in which the spatial 
correlation is homogenous. This is done using Monte Carlo 
significance test given by Brunsdon et al. (1998). 
3.1.2 Sample selection 
Let ot; denote the probability of selection of i unit in the sample. 
The sample is drawn sequentially by assigning weights based on 
spatial correlation and size of the auxiliary variable, varying at 
each draw. The first unit is selected by probability proportional to 
size (PPS) sampling and the remaining n-1 units are drawn 
sequentially by assigning the following weights: 
Unit Weight 
2 Ui, -0-p312)x5 ; 
n U, -0- B^» - pfo)... (- go x. 
where dj; is the distance in terms of order of neighbourhood. 
3.1.3 The Proposed Estimator 
Let: yj. Ya be the values of the unit drawn at the first, 
second... n" draw respectively and let 0, ..,&, be the probabilities 
of selection of. y, ,.., Y, respectively. Let s: yes s. denote the 
sample set containing the units selected after first, second,...,n 
draws respectively, such that, s; - (yi), s - (yb.y2); nis 
* 
Sn -lyLY2.Y3 ........ Yn}- 
An unbiased estimator of population mean, denoted by T is given 
by, 
IAPRS & SIS, Vol.34, Part 7, “Resource and Environmental Monitoring”, Hyderabad, India, 2002 
UnXn 
Yun 
. * 
1S5. 
ico 
where, an = and 
1 
on =| years ian E 
on 
The form of estimator T, is similar to the ordered estimator given 
by Des Raj (1956). On similar lines, the estimate of variance of 
the estimator T, that is also an ordered estimator can be expressed 
as: 
  
n(n 
n 
vTp- — 6 -1p? x 
i=l 
The above explained CUBSS technique was extended to Stratified 
sampling. And was termed as Stratified Contiguous Unit Based 
Spatial Sampling (Stratified CUBSS) technique. 
3.2 Simulation Study 
A simulation study has been conducted for testing the 
performance of the proposed spatial sampling techniques and to 
compare them with the traditional sampling designs generally 
used for spatial data. The irrigated area (Y) of the village is 
estimated based on the total cultivated area (X), which is treated 
as the auxiliary character for the study. In this simulation study 
1000 samples of sizes 30, 50, 75 and 100 have been selected 
adopting different sampling procedures and corresponding 
estimators are obtained. Along with the proposed estimators other 
estimators are obtained using (i) Simple Random Sampling 
without Replacement (SRSWOR) Ti, (ii) Stratified 
SRSWOR(T,), (iii) Dependent Unit Sequential Technique 
(DUST) Ts (Arbia, 1993) and (iv) Stratified DUST(Ts). The 
formulae used for estimators, their variance and estimate of 
variance are standard ones. The pictorial representation of the 
implementation of the proposed sampling technique using GIS is 
shown in Fig. 1. 
    
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