A simulation study with log, Box-Cox, and dual-power transformation on handling curvilinear relationship in small area estimation

5th International Seminar on Sciences

自然科学（总论）

Bodro, D.K.^1 ; Sartono, B.^1 ; Sadik, K.^1

Department of Statistics, Institut Pertanian Bogor, Bogor, Indonesia^1

关键词: Auxiliary variables;    Dual power;    Mean absolute percentage error;    Monotonic functions;    Positive real;    Real number;    Simulation studies;    Small area estimation;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/299/1/012029/pdf
DOI  :  10.1088/1755-1315/299/1/012029

学科分类：自然科学（综合）

来源: IOP

【 摘 要 】

A standard small area estimation method may fail to produce reasonable estimates when the normality assumption is not met or the relationship between the interest parameter and the auxiliary variables is not linear. A logarithm transformation has been widely used to help this issue and works well for some cases. However, it may not be generally valid so that some transformation such as Box-Cox (BC) and dual power (DP). This paper discusses a simulation study on how BC and DP could overcome circumstances where those aforementioned problems are there in the data. Several different forms of the relationship were studied and the study revealed that BC and DP transformation are the recommended methods because they produced smaller Mean Absolute Percentage Error (MAPE) values than ones without transformation or using logarithm transformation. Even if DP does not consistently provide the lowest value, but technically, DP can overcome truncated problems that occur in BC. The findings of this work indicate that this new transformation, DP, is proposed to be the best transformation to overcome the abnormality of an interesting variable because this transformation produces a monotonic function that has a domain of positive real numbers (+) and range of whole real numbers ().