AN EFFICIENT SHORT CUT METHOD FOR COMPUTING THE COEFFICIENTS OF THE BEST LINEAR UNBIASED ESTIMATOR OF POPULATION MEAN FOR CORRELATED RANDOM VARIABLES

Abstract

An efficient short cut method for computing the coefficients of the best linear unbiased
estimator (BLUE) of the population mean for correlated random variables with a defined
covariance structure has been proposed in the paper. For correlated random variables with a
moving average process of order one covariance structure, the existing method involves
minimizing the variance of BLUE subject to the linear constraint that arises from the
unbiasedness condition. To propose a new efficient short cut method, the symmetric pattern
of BLUE’s vector of coefficients or weights was generalized using mathematical induction.
The existing quadratic programming problem was further simplified to obtain an efficient
short cut computational method by adding the developed symmetric pattern of the vector of
coefficients, along with the unbiasedness condition, as constraints. Hence, it reduces the
computational time and complexity involved in evaluating the covariance and/or correlation
matrix of the correlated variables. The efficacy of the proposed efficient method was
demonstrated with ease through the applicability of the method to compute the algebraic
expressions of weights or coefficients of BLUE when the number of observations; kn2 and
12kn at fixed 8,...,2,1k . Then, the estimates of BLUE’s weights when the number of
observations; 2;12kkn were computed as an illustrative example. Empirical example
on BLUE’s weights computation was demonstrated using four purposively selected real life
data sets (each with varying sample sizes) that admit moving average process of order one.
The results indicate that BLUE’s weights computed using the proposed method estimate
population mean with high precision than the arithmetic mean (AM) across the varying
sample sizes of the four purposively selected data sets.