NORMAL RATIO IN MULTIPLE IMPUTATION BASED ON BOOTSTRAPPED SAMPLE FOR RAINFALL DATA WITH MISSINGNESS

Abstract

The existence of missing values in rainfall data series is inevitably affects the quality of the data.
This problem will influence the results of analysis and subsequently provide imprecise information to the
hydrological and meteorological management. A practical and reliable approach is needed in developing
estimation methods to impute the missing values. Single imputation is the most commonly used approach for
missing values, but, it encounters with the limitation of not considering the uncertainty and natural variability in
missing data imputation. Thus, this study has proposed multiple imputation approach based on bootstrap samples
in order to overcome the limitation of single imputation approach. Three normal ratio estimation methods are
implemented using the proposed approach. The performances of the estimation methods are evaluated at six
different levels of missingness. Complete 40 years daily rainfall data from four meteorology stations were
considered for the analysis purpose with Johor Bahru station was selected as the target station. The results of the
proposed approach were compared to the results obtained from single imputation approach and the widely
known built in software for multiple imputation, Amelia II package, in assessing the performance of proposed
approach. The results showed that all estimation methods that implemented using proposed approach provided
the most accurate estimation results at all percentages of missingness. This proves the advantage of adaption of
variability and uncertainty element in the proposed approach in estimating the missing rainfall data at the area of
the current study.