Page 352 - Contributed Paper Session (CPS) - Volume 7

CPS2125 Dian Handayani et al.

Small area estimation for linear parameter under
a spatial unit-level lognormal model
Dian Handayani 1,2,4 , Henk Folmer , Khairil Anwar Notodiputro , Anang
4
2,3
5
2
4
4
Kurnia , Asep Saefuddin , Arno J. Van der Vlist , I Wayan Mangku
1. Department of Statistics, Faculty of Mathematics and Natural Sciences, State University of
Jakarta, Indonesia.
2. Department of Economic Geography, Faculty of Spatial Sciences, University of Groningen,
The Netherlands.
3. College of Economics and Management, Northwest Agriculture and Forestry University,
Yangling, China.
4. Department of Statistics, Faculty of Mathematics and Natural Sciences, IPB University,
Indonesia.
5. Department of Mathematics, Faculty of Mathematics and Natural Sciences, IPB University,
Indonesia.

Abstract
In this paper, we propose the extended Spatial Empirical Best Prediction (SEBP)
to estimate linear parameter, i.e. small area mean, whenever variable of
interest has positively skewed distribution and spatial dependence among
small areas are taken into account. The extended SEBP improve the SEBP
(Handayani, 2018) by estimating values of variable of interest with the
conditional expectation of variable of interest given the data and random area
effects. A parametric bootstrap is proposed for the estimation of mean square
error of estimates of linear parameter. Our simulation studies indicate that the
relative performance of the SEBP that we propose is outperform in terms of
bias and mean square error.

Keywords
spatial empirical best predictor; skewed data; spatial dependence; parametric
bootstrap.

1. Introduction
Indirect estimation method in Small Area Estimation (SAE) is usually
model-based method. The standard SAE method is developed under linear
mixed model which assumes normality on variable of interest and
independence among random area effect. Berg and Chandra (2014) proposed
Empirical Best Predictor (EBP) to estimate linear parameter, i.e population
mean, for variable of interest which has positively skewed distribution but
among small areas are still assumed to be independent. Handayani et al (2018)
developed the Spatial Empirical Best Predictor (SEBP) to estimate population
mean, for positively skewed variable of interest and the spatial dependence
among random area effect are taken into account. By using the SEBP,

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