Munir Mahmood

On the confidentiality guaranteed under randomized response sampling : A comparison with several new techniques

In this paper, three simple alternative randomized response models are proposed to be used in the situation where Moors (1971) model fails as shown by Mangat et al. (1997). The proposed estimators are shown to be more efficient than the estimator proposed by Greenberg et al. (1969).

Classroom note: An inductive derivation of Stirling numbers of the second kind and their applications in statistics

An inductive method has been presented for finding Stirling numbers of the second kind. Applications to some discrete probability distributions for finding higher order moments have been discussed.

The mean squared error of the likelihood based estimating equations in the general linear model

Mahmood and King (17) revealed that the marginal likelihood has the inherent property of unbiased estimating equa- tions amongst a range of modified likelihood methods. In this paper we extend our investigation to deriving the mean squared error of the scores of the profile likelihood, the marginal likelihood, the conditional profile likelihood and the conditional profile restricted likelihood. In terms of minimum mean squared error, the estimating equation from the conditional profile restricted likelihood emerged as the preferred method. This provides further support to the implications of thefindings of poor small-sample properties of Lagrange Multiplier (LM) tests in the literature which are based on biased estimating equations or having a larger mean squared error of the scores. We demonstrate that the relative error of the mean squared error between the conditional profile restricted and the marginal likelihood methods is negligible for increasingly larger samples. Amongst the unbiased estimating equations the minimum mean squared error criteria provides a clear choice of selecting the estimating equation for the purpose of estimation and testing.