Page 351 - Contributed Paper Session (CPS) - Volume 2

CPS1885 Karuna G. R. et al.
iterative algorithm by [8] which minimizes the total sample size required to
achieve a target level of precision, the Geometric method by [7] and the
Random Search method of [9]. All methods stated herein depend on a fixed
total sample size () and do not consider the cost of sampling (), which is
divided into stratum costs ( ; ℎ = 1, 2, . . . , ). They also do not achieve
ℎ
optimality in OSB points or optimal sample allocations.
In this paper, we employ the method of stratification proposed by [11],
which is based on the probability distribution functions of the continuous
study variable. The problem of determining OSS based on cost is formulated
as a mathematical programming problem (MPP) and solved by the dynamic
programming (DP) technique proposed by [10]. The method computes OSS
which depends on the estimated frequency distribution of the study variable
if data is known and can even be hypothesized if it is not available to the
surveyor especially when sampling is at the planning stage. The number of
strata () and per unit stratum costs ( ; = 1, 2, . . . , ) are fixed in advance.
ℎ

2. Methodology
In designing a stratified sampling survey using past or recent survey data,
this technique uses the stratum cost to determine the OSB and OSS based on
a study variable. Methodologies involved in the formulation of the
stratification problem into an MPP will be depicted using a real home equity
loans credit data set called HMEQ [15], which presents information on 5, 960
home equity loans where the obligor uses the equity of his or her home as the
underlying collateral. We will consider the study variable mortdue, which is the
amount due on the existing mortgage, as the main study variable.
Let the target population of mortdue () be stratified into strata where
the estimation of its mean is of interest. If a simple random sample of size
ℎ
is to be drawn from ℎ stratum with sample mean ̅ , then the stratified
ℎ
ℎ
sample mean, ̅ , is given by

̅ = ∑ ̅ , (1)
ℎ
ℎ

ℎ=1

where is the proportion of the population contained in the ℎ
ℎ
ℎ
stratum. Equation (1) is an unbiased estimate of the population mean with
̅
ℎ
variance

1 1
2 2
(̅ ) = ∑ ( − ) . (2)
ℎ ℎ

ℎ ℎ
ℎ=1

The total cost of a survey may be expressed as

= + ∑ , (3)
ℎ ℎ
0
ℎ=1
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