In this study, we proposed an alternative biased estimator. The linear regression model might lead to ill-conditioned design matrices because of the multicollinearity and thus result in inadequacy of the ordinary least squares estimator (OLS). Scientists have developed alternative estimation techniques that would eradicate the instability in the estimates. Several biased estimators such as Stein estimator, the ordinary ridge regression (ORR) estimator, the principal components regression (PCR) estimator. Liu developed a Liu estimator (LE) by combining the Stein estimator with the ORR estimator. Since both ORR and LE depend on OLS estimator, multicollinearity affects them both. Therefore, the ORR and LE may give misleading information in the presence of multicollinearity. To overcome this problem, Liu introduced a new estimator, which is based on k and d biasing parameters, the authors worked on developing an estimator that would still have the valuable characteristics of the Liu-type estimator (LTE) but have a smaller bias. We are proposing a modified jackknife Liu-type estimator (MJLTE) that was created by combining the ideas underlying both the LTE and JLTE. Under mean square error matrix criteria, the MJLTE is superior to Liu-type estimator (LTE) and jackknifed Liu-type estimator (JLTE). Finally, a real data example and a Monte Carlo simulation are also given to illustrate theoretical results.
Part of the book: Statistical Methodologies
The objective of a meta-analysis is usually to estimate the overall treatment effect and make inferences about the difference between the effects of the two treatments. Meta-analysis is a quantitative method commonly used to combine the results of multiple studies in the medical and social sciences. There are three common types of meta-analysis. Pairwise, Multivariate and Network Meta-analysis. In general, network meta-analysis (NMA) offers the advantage of enabling the combined assessment of more than two treatments. Statistical approaches to NMA are largely classified as frequentist and Bayesian frameworks Because part of NMA has indirect, multiple comparisons, As reports of network meta-analysis become more common, it is essential to introduce the approach to readers and to provide guidance as to how to interpret the results. In this chapter, the terms used in NMA are defined, relevant statistical concepts are summarized, and the NMA analytic process based on the frequentist and Bayesian framework is illustrated using the R program and an example of a network involving diabetes treatments. The aim of the article is to compare the basic concepts and analyzes of network meta-analysis using diabetes data and the treatment methods used.
Part of the book: Computational Statistics and Applications