A METHOD OF ESTIMATING MISSING VALUES FOR POPULATION
MEAN ESTIMATION
Nuanpan Nanguse; Phanuphong Thaweekaew
Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of
Technology North Bangkok,
1518 Pibulsongkram Road, Bangsue, Bangkok 10800, Thailand; E-mail:nmt@kmutnb.ac.th
Abstract
The problem of estimating the population mean using auxiliary information when
some observations in the sample data are missing, is considered. We propose a new
method for estimating the population mean that adjusts Rueda et al.’s estimator,
which was proposed by Rueda et al. [Rueda et al., Estimation of the population mean
using auxiliary information when some observations are missing, International
symposium on applied stochastic models and data analysis, 2005, May 17-20, Brest
France]. They proposed a new estimator for the mean of the variable of interest, using
all known data for principal and auxiliary variables. This research considers a
composite imputation method called nearest neighbor ratio imputation to estimate
missing data using an auxiliary variable, and compares it with the two imputation
methods: nearest neighbor imputation and ratio method of imputation. We also used
two estimators to estimate missing values (when some observations are missing in
both variables) called regression type estimators [Singh S., Advanced sampling theory
with applications, 2003, Vol. II. Kluwer Academic Press Publishers] which impute a
value by the regression line value. Five methods were compared in a simulation study
using population (X,Y) values of size (N) 1,000 and 5,000 for different sample sizes
and correlation coefficients between X and Y. In a sample, 10, 20 or 30 percent of the
cases were be randomly designated as missing. The results show that the new methods
give a smaller mean absolute percentage error when compared with the Rueda et al.
method in every case.
Keywords : auxiliary information; missing data; nearest neighbor ratio imputation;
nearest neighbor imputation; ratio method of imputation; regression type estimators