Application of the multivariate depth-based method for ranking the performance of judiciary

Document Type : Original Scientific Paper

Author

Institute of Judiciary Research‎, ‎Tehran‎, ‎Iran

Abstract

Evaluating the performance and ranking of the judiciary of the provinces periodically is always of interest‎. ‎This problem can be done with univariate approaches; But considering many variables involved in this matter‎, ‎the use of multivariate methods is more justified‎. ‎A new method for this is ranking based on the depth concept‎. ‎In this paper‎, ‎the performance of prosecutors' offices‎, ‎criminal courts and appeals courts of the provinces have been ranked over one year based on two indicators; case processing rate and the case congestion rate‎, ‎employing the depth multivariate method‎. ‎Evaluating the results of ranking intuitively confirms the appropriateness and rationality of this approach.

Keywords

Main Subjects


Arnold, B.C., Castillo, E. and Sarabia, J.M. (2009a). Multivariate order statistics via multivariate concomitants. Journal of Multivariate Analysis, 100:946–951.
Arnold, B.C., Castillo, E. and Sarabia, J.M. (2009b). On multivariate order statistics, Application to ranked set sampling. Computational Statistics and Data Analysis, 53:4555–4569.
Bairamov, I.G. and Gebizlioglu, O.L. (1998). On the ordering of random vectors in a norm sense. Journal of Applied Statistical Science, 6:66–77.
Bairamov, I.G. (2006). Progressive type 2 censored order statistics for multivariate observations. Journal of Multivariate Analysis, 97:797–809.
Barnett, V. (1976). The ordering of multivariate data. Journal of Royal Statistical Society A, 139:318–343.
Dandurand, Y., MacPhail, L. and Kittayarak, K. (2015). Justice Indicators and Criminal Justice Reform. International Centre for Criminal Law Reform and Criminal Justice Policy, Vancouver, British Columbia, Canada.
Liu, R.Y. and Singh, K. (2006). Rank tests for multivariate scale difference based on data depth. DIMACS Series Discrete Mathematical Theory and Computer Science, 72:17–35.
Liu, R.Y. and Singh, K. (1993). A quality indexed based on data depth and multivariate rank tests. Journal of American Statistical Association, 88:252–260.
Liu, R.Y., Parelius, J.M. and Singh, K. (1999). Multivariate analysis by data depth: descriptive statistics, graphics and inference. Annals of Statistics, 27:783–858.
Pokotylo, O., Mozharovskyi, P. and Dyckerhoff, R. (2016). Depth and depth-based classification with R-package ddalpha. Preprint. arXiv:1608.04109.
Tat, S. and Faridrohani, M.R. (2021). A new type of multivariate records: depth-based records. Statistics, 55:296–320.
Tukey, J.W. (1975). Mathematics and Picturing Data. Proceedings of the International Congress on Mathematics. Canadian Mathematics Congress.
Zuo, Y. and Serfling, R. (2000). General notions of statistical depth function. The Annals of Statistics, 28:461–482.