R. Minkah (BSc (Ghana) , MSc (Uppsala), PhD (Ghana))

Research interest

My research interest is in Statistics of Extremes and its applications in real-life problems. My research in this area has focused on getting reduced-bias estimators of the tail index of distributions and the estimation of high quantiles. Part of my work focuses on estimation of the tai index and extreme quantiles in the presence of censoring and covariate information. In recent years I have focused on robust statistics of extremes with interest in estimators that are less sensitive to very outlying observations or deviations from assumed parametric distributions. In addition, I have research interest in computational statistics – bootstrap and other resampling methods.

Current research/project(s)
i) Extreme Value Theory for Binary Rare Events

Logistic regression provides the most common regression method for the estimation of binary dependent variable. However, when the dependent variable represents a rare event, the logistic regression model shows relevant drawbacks. To overcome this difficulty, we intend to use as a link function obtained from the quantile function of an extreme value distribution. In such an extreme value regression model, attention is paid to the tails of the underlying distribution of the dependent variable as the link function is asymmetric and hence the response curve will approach zero at a different rate as it approaches one. It is expected that modelling the binary response in this way will enable us to predict binary rare events such as default probabilities and bankruptcy.

ii) Threshold selection in the Peaks-Over Threshold method

The selection of threshold for fitting a generalised Pareto distribution is a major issue for researchers in Extreme Value Analysis. In the case of the constant threshold, several authors have looked at different approaches to obtain the threshold value including stability plots in graphs, asymptotic mean square errors, among others. In this work, we investigate a covariate dependent threshold based on expectiles. The expectile threshold better spans the covariate space in contrast to the constant threshold and the quantile regression. We compare the expectile threshold with the existing thresholds in a simulation study involving an exponential growth data for estimating the tail index of the Generalised Pareto distribution.

iii) Robust Extremes (joint with Prof. T. de Wet and Prof. Abhik Ghosh).

Extreme value distributions have been used to model several phenomena but the         issue of robustness of the extreme value analysis and its applications has not received much attention to the best of our knowledge.  In this case, we envisage computing worst case scenarios over model uncertainty region in terms of some measures of divergence. Such a view will enable us to forecast extreme events through some data-driven method that is robust to model uncertainties.  We consider a family of distributions which lie within the neighbourhood of the asymptotic distribution for exceedances over a given threshold. Therefore, by using some distance measures of divergence between the reference distribution and the new family of models, we can compute a worse case estimate for extreme events. We will be investigating the use of different measures of divergence in estimating the parameters in Extreme Value Theory using measures that lead to estimators that are robust to deviations from model assumptions or outliers.

Past research projects

Robust Estimation of Pareto-Type Tail Index through an Exponential Regression Model. One year, University of Ghana BANGA-Africa Project

Awards

• Awarded the University of Ghana-Carnegie Corporation BANGA-Africa conference travel grant of $1500 to attend the South African Statistical Association conference, 2019.
• Awarded $7,920 BANGA-Africa Post-doctoral grant for 3 months’ collaborative research with Prof. T. de Wet, Stellenbosch University, South Africa in 2018
• University of Ghana Vice-Chancellor’s Award for Best Doctoral Thesis for the Sciences, 2016.
• University of Ghana-Carnegie Corporation PhD grant of $60,000.00, 2012-2016
• Obtained several Conference grants from University of Ghana, Stellenbosch University and African Institute of Mathematics, Ghana between 2013-2019.

Recent publications

i. Minkah, R., de Wet, T., and Ghosh, A.  (2020).  Robust Estimation of Pareto-Type Tail Index through an Exponential Regression Model. Manuscript submitted for publication.
ii. Dzidzornu, S. K. and Minkah, R. (2020). Assessing the Performance of the Discrete Generalised Pareto Distribution in Modelling Non-Life Insurance Claims. Manuscript submitted for publication.
iii. Minkah, R. and de Wet T. (In press). Constant verses Covariate dependent Threshold in the Peaks-Over Threshold Method. Journal of Applied Probability and Statistics. Preprint available at arXiv:1812.03432v1
iv. Minkah, R. and T. de Wet. (2020). Tail Index Estimation of the Generalised Pareto Distribution
using a Pivot from a Transformed Pareto Distribution. Science and Development. 4(1), 19-27.
v. Minkah, R., & de Wet, T. (2019). Comparison of Confidence Interval Estimators: An Index Approach. Journal of Applied Probability and Statistics. 9(1): 31-55.
vi. Minkah, R., de Wet, T., & Nortey, E. N. N. (2018). A Simulation Comparison of Estimators of Conditional Extreme Value Index under Right Random Censoring. African Journal of Applied Statistics.  5(1), 337-349.
vii. Minkah, R., de Wet, T., & Doku-Amponsah, K. (2018). On Extreme Value Index Estimation under Random Censoring. African Journal of Applied Statistics. 5(2): 421-447.
viii. Minkah, R. and T. de Wet. (2018). Estimation of the Tail Index of a Generalised Pareto Distribution using a Pivot from a Transformed Pareto Distribution. In A. Göktaş, Ö. Akkuş, Ö. gürünlü, N. G. Narin, E. Doğu, N. G. Dinçer and S. Mermi, M. O. Yalçin and B. Durmuş (Eds.), 11. International Statistics Days Conference (pp. 598-609). Bogrum, Turkey. Turkish Statistical Association.
ix. Adu-Acheampong, S., Samways, M. J., Landmann, T., Kyerematen, R., Minkah, R., Mukundamago, M., & Moshobane, C. M. (2017). Endemic grasshopper species distribution in an agro-natural landscape of the Cape Floristic Region, South Africa. Ecological Engineering, 105, 133-140.
x. Minkah, R. (2016). An application of extreme value theory to the management of a hydroelectric dam. SpringerPlus 5 (1), 1-12.
xi. Nortey, E. N., Ansah-Narh, T., Asah-Asante, R., & Minkah, R. (2015). A Markov chain Monte Carlo (MCMC) methodology with bootstrap percentile estimates for predicting presidential election results in Ghana. SpringerPlus, 4(1), 1-12.

Professional membership(s)
a) Statistical Pan African Society
b) South African Statistical Association
c) International Society for Business and Industrial Statistics
d) International Statistical Institute
e) Ghana Statistical Association
f) Statistical Pan African Society