Outliers in a statistical analysis strongly affect the performance of the ordinary least squares, such outliers need to be detected and extreme outliers  deleted. Thisp is aimed at proposing a Redescending M-estimator which is more efficient and robust compared to other existing methods. The results show that the proposed method is effective in detection and deletion of extreme outliers compared to the other existing ones.

In this article, some non-bayesian estimation procedures of the Exponentiated Power Lindley-Logarithmic Distribution for modeling real life data are considered. A simulation study is carried out to determine the best among others using the root meas squared error values. Real life data are used to substantiate the result from the simulation study. It was discovered from simulation study and real data that the weighted least squares estimation procedure is the best method for estimating the parameters of the Exponentiated Power Lindley-Logarithmic distribution.

In this paper, we proposed the generalized method and algorithms developed for estimation of parameters and best model fits of log linear model for n-dimensional contingency table. For purpose of this work, the method was used to provide parameter estimates of log-linear model for three-dimensional contingency table. In estimating parameter estimates and best model fit, computer programs in R were developed for the implementation of the algorithms. The iterative proportional fitting procedure was used to find the parameter estimates and goodness of fits of the log linear model. Akaike information criteria (AIC) and Bayesian information criteria (BIC) were used to check the adequacy of the model of the best fit. Secondary data were used for illustration and the result obtained showed that the best model fit for three-dimensional contingency table had a gene-rating class: [CA, AB]. This showed that the best model fit had sufficient evidence to fit the data without loss of information. This model also revealed that breed was independent of chick loss given age. The best model in harmony with the hierarchy principle is

This work estimated the standard error of the maximum likelihood estimator (MLE) and the robust estimators of the exponential mixture parameter (θ) using the influence function and the bootstrap approaches. Mixture exponential random samples of sizes 10, 15, 20, 25, 50, and 100 were generated using 3 mixture exponential models at 2%, 5% and 10% contamination levels. The selected estimators namely: mean, median, alpha-trimmed mean, Huber M-estimate and their standard errors (Tn ) were estimated using the two approaches at the indicated sample sizes and contamination levels. The results were compared using the coefficient of variation, confidence interval and the asymptotic relative efficiency of Tn in order to find out which approach yields the more reliable, precise and efficient estimate of Tn. The results of the analysis show that the two approaches do not equally perform at all conditions. From the results, the bootstrap method was found to be more reliable and efficient method of estimating the standard error of the arithmetic mean at all sample sizes and contamination levels. In estimating the standard error of the median, the influence function method was found to be more effective especially when the sample size is small and yet contamination is high. The influence function based approach yielded more reliable, precise and efficient estimates of the standard errors of the alpha-trimmed mean and the Huber M-estimate for all sample sizes and levels of contamination although the reliability of the bootstrap method improved better as sample size increased to 50 and above. All simulations and analysis were carried out in R programming language.

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