Peter Nyamuhanga Mwita

On the Estimation and Properties of Logistic Regression Parameters

Logistic regression is widely used as a popular model for the analysis of binary data with the areas of applications including physical, biomedical and behavioral sciences. In this study, the logistic regression model, as well as the maximum likelihood procedure for the estimation of its parameters, are introduced in detail. The study has been necessited with the fact that authors looked at the simulation studies of the logistic models but did not test sensitivity of the normal plots. The fundamental assumption underlying classical results on the properties of MLE is that the stochastic law which determines the behaviour of the phenomenon investigated is known to lie within a specified parameter family of probability distribution (the model). This study focuses on investigating the asymptotic properties of maximum likelihood estimators for logistic regression models. More precisely, we show that the maximum likelihood estimators converge under conditions of fixed number of predictor variables to the real value of the parameters as the number of observations tends to infinity.We also show that the parameters estimates are normal in distribution by plotting the quantile plots and undertaking the Kolmogorov -Smirnov an the Shapiro-Wilks test for normality,where the result shows that the null hypothesis is to reject at 0.05% and conclude that parameters came from a normal distribution.

Statistical techniques for modeling extreme price dynamics in the energy market

Extreme events have large impact throughout the span of engineering, science and economics. This is because extreme events often lead to failure and losses due to the nature unobservable of extra ordinary occurrences. In this context this paper focuses on appropriate statistical methods relating to a combination of quantile regression approach and extreme value theory to model the excesses. This plays a vital role in risk management. Locally, nonparametric quantile regression is used, a method that is flexible and best suited when one knows little about the functional forms of the object being estimated. The conditions are derived in order to estimate the extreme value distribution function. The threshold model of extreme values is used to circumvent the lack of adequate observation problem at the tail of the distribution function. The application of a selection of these techniques is demonstrated on the volatile fuel market. The results indicate that the method used can extract maximum possible reliable information from the data. The key attraction of this method is that it offers a set of ready made approaches to the most difficult problem of risk modeling.