Small Area Estimation - Sampling Spatial Units for Agricultural Surveys - page 267

Chapter 11
Small Area Estimation

11.1 Introduction

Sample survey methods, whether they are conducted by government organizations
or by private entities, are used to provide direct estimates for a total of a variable y
for a population under investigation and for sub-populations or domains (S¨rndal
et al. 1992 , Chap. 10 ).
An important aim of many statistical agencies is to efficiently estimate popula-
tion characteristics for small domains or areas. The term small area (SA) typically
refers to a small geographically defined domain such as a county, municipality, or
administrative division, a spatial population such as a type of crop or a particular
economic activity, or a subgroup of people with the same sex, race, or other
characteristics. These smaller domains are contained within a large domain. We
cannot produce reliable statistics for these SAs because there are certain limitations
on the available data. Some synonymous terms are small domain, minor domain,
local area, and small sub-domain (see Rao 2003 ).
Defining statistical units (compare Sect. 2.2 ) is a key issue in territorial empirical
analysis. In fact, spatial units can often differ in size and in many other important
economic characteristics. Therefore, different choices for spatial statistics can have
serious effects on sampling design, statistical analysis, and policy implications. The
appropriate definition of the problems deriving from the aggregation of spatial units
is often denoted as Modifiable Areal Unit Problem (Openshaw 1977 ). MAUP
considers uncertainties that arise when choosing an alternative number of zones
and the implications that this entails for spatial analysis (Openshaw and Taylor 1981 ).
The effects of MAUP can be divided into two main components: the scale effect
and the zone effect . The scale effect is the variations in numerical results that occur
due to the number of zones and the spatial resolution. The conclusions will depend
on the selected spatial scale. Furthermore, the correlation among two or more
variables strongly depends on the territorial scale. In applications on agricultural
and environmental data, spatial dependence usually decreases as the number of