English abstract
A great deal of research in the statistical literature has given rise to the existence of bias
in inferential procedures based on the maximum likelihood estimators. Moreover, this is a
matter of serious concern when the data contains some missing values. The magnitude of
such bias can significantly affect the study conclusions; if large, misleading conclusions
will be drawn, the sample size will be reduced, as well as the statistical power. In the
present thesis, a review of some methods for handling missing data and bias reduction
with some application has been done. While we attempted to reduce the impact of bias in
estimated parameters when the data is incomplete, we proposed a penalized-based method
to reduce bias in the estimated model parameters under data missing at random mech anism. We applied the expectation-maximization principle with weights, and penalized
the log-likelihood function with LogF(1,1) for the logit model. Using the Louis(1982)
method, we derived the information matrix, while a closed form for the exact bias of the
estimated parameter was derived following the Cox and Snell (1968) equation. Further,
to facilitate usage of the proposed method, a new BRLFP R Package has been developed.
A combination of simulation studies and real-life data problems were used to validate
the proposed bias reduction method. Findings from these validation studies consistently
show significant reductions in the standard errors of the estimates when compared with
other classical bias reduction methods for the missing at random data mechanism. Penalizing the log-likelihood function with the LogF(1,1) was found to generate more efficient
parameter estimates for the logistic model under the missing at random mechanism.
