Page 321 - Contributed Paper Session (CPS) - Volume 6

CPS1942 Daniel D. M. P.

Estimation using probability proportional to
aggregate size sampling in heterogeneous
populations
Daniel David M. Pamplona
University of the Philippines, Philippines

Abstract
Estimation using Probability Proportional to Aggregate Size (PPAS) is
compared with traditional design-unbiased techniques under different
population scenarios. The study considers both standard error and relative
bias of total estimates for comparison. Heterogenous populations were
simulated by exploring varying behaviours of an auxiliary variable and its
relationship with the target variable. Results show that the optimality of PPAS
estimates improve as the linear association between the target variable and
auxiliary variable increase. Furthermore, PPAS estimates are more stable under
large variability in population.

Keywords
sampling rate; covariate effect; model fit; auxiliary variable; standard error;
absolute percentage error

1. Introduction
Estimation methods for the total in survey sampling have developed over
the years. Among these methods are design-unbiased and model-assisted
techniques. Design-unbiased methods generate estimates based on the
sampling distribution induced by the sample selection procedure. In other
words, the method of sample selection determines the confidence in the
estimates produced. This method, however, works best only when the
sampling procedure has been religiously implemented, which in most cases,
pose a challenge due to many practical reasons such as: unavailability of
respondents, logistical limitations, absence of population frame, etc. Model-
assisted estimation is a procedure of generating estimators with an aid of a
model, usually in linear form. Inferences made about the population is still
based on the sampling method used, but the estimation still works even if the
model does not fit the data well. Aside from the target variable alone, this
method partly relies on other information from the population to motivate the
estimate.
Given the two methods of interest, several attempts have been made to
find the criteria for comparing the various strategies while attempting to
obtain optimal results from a sample survey. In this paper we explore on the
use of the model-assisted estimation using Probability Proportional to

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