Academia.eduAcademia.edu

Figure 7 – uploaded by Dariush Khezrimotlagh

See full PDFdownloadDownload figure
The 0.1-KAM lowest targets, shown by small multiplication signs, illustrate the effects on the Farrell frontier by introducing 10 percentage errors in DMUs’ input and output values. Indeed, the effects on the Farrell frontier were commensurately considered for each evaluated DMU by selecting ey and ef as 0.1 x x,, and 0.1 x y;,, respectively, and can be considered as variations of the sample, which was one of the concerns of Grosskopf (1996). Khezrimotlagh, D. (2015). How to detect outliers in data envelopment analysis by Kourosh and Arash method. arXiv preprint arXiv: 1503.02548

Figure 7 The 0.1-KAM lowest targets, shown by small multiplication signs, illustrate the effects on the Farrell frontier by introducing 10 percentage errors in DMUs’ input and output values. Indeed, the effects on the Farrell frontier were commensurately considered for each evaluated DMU by selecting ey and ef as 0.1 x x,, and 0.1 x y;,, respectively, and can be considered as variations of the sample, which was one of the concerns of Grosskopf (1996). Khezrimotlagh, D. (2015). How to detect outliers in data envelopment analysis by Kourosh and Arash method. arXiv preprint arXiv: 1503.02548

Related Figures (7)

The targets of KAM, that is, the highest (x*, y*), the best technical (x*, y*) and the lowest (x*, y*) efficient targets with e-Degree of Freedom (€-DF), the highest KA?!, the best technical KA*! and the lowest KA*! efficiency scores as well as sensitivity score 52! with e-DF, respectively are given by:
The targets of KAM, that is, the highest (x*, y*), the best technical (x*, y*) and the lowest (x*, y*) efficient targets with e-Degree of Freedom (€-DF), the highest KA?!, the best technical KA*! and the lowest KA*! efficiency scores as well as sensitivity score 52! with e-DF, respectively are given by:
Let us suppose 100 DMUs depicted in Figure 1 with one input and one output when at least one of the types (1)-(IV) happen. This example was selected to be similar to the work of Simar (2007) and Simar and Zelenyuk (2011) which claimed the weakness of DEA to detect outliers. From the figure, it is clear that there are some outliers and extreme values which effect on the frontier.
Let us suppose 100 DMUs depicted in Figure 1 with one input and one output when at least one of the types (1)-(IV) happen. This example was selected to be similar to the work of Simar (2007) and Simar and Zelenyuk (2011) which claimed the weakness of DEA to detect outliers. From the figure, it is clear that there are some outliers and extreme values which effect on the frontier.
Now let us see which DMUs are A-R in the sample. Figure 3 depicts DMUs A-R among observed DMUs. As can be seen, KAM nicely detects outliers while it simultaneously ranks and benchmarks them without the computational complexities of current hybrid technologies. We also selected the half values of minimum input and minimum output of DMUs to define ey and ¢;', respectively, in order to have the same commensurate effects on the Farrell frontier for evaluating each DMU (Khezrimotlagh et al. 2013a), and again found DMUs A-R as outliers according to the parts (1), (11) and (iii).
Now let us see which DMUs are A-R in the sample. Figure 3 depicts DMUs A-R among observed DMUs. As can be seen, KAM nicely detects outliers while it simultaneously ranks and benchmarks them without the computational complexities of current hybrid technologies. We also selected the half values of minimum input and minimum output of DMUs to define ey and ¢;', respectively, in order to have the same commensurate effects on the Farrell frontier for evaluating each DMU (Khezrimotlagh et al. 2013a), and again found DMUs A-R as outliers according to the parts (1), (11) and (iii).
Figure 2: KAM outcomes for 100 DMUs. Khezrimotlagh, D. (2015). How to detect outliers in data envelopment analysis by Kourosh and Arash method. arXiv preprint arXiv: 1503.02548
Figure 2: KAM outcomes for 100 DMUs. Khezrimotlagh, D. (2015). How to detect outliers in data envelopment analysis by Kourosh and Arash method. arXiv preprint arXiv: 1503.02548
Figure 4: Detecting best efficient DMUs by KAM. Khezrimotlagh, D. (2015). How to detect outliers in data envelopment analysis by Kourosh and Arash method. arXiv preprint arXiv: 1503.02548. The polygon chart of technical efficiency score with 0-DF is gradually decreased. As it depicted with two dotted vertical ellipses, DMUs ‘a’-‘d’, ‘g’ and ‘h’ have simultaneously a good value of technical efficiency score with 0-DF, a good value of best technical and lowest efficiency score with 0.1-DF, a lesser difference between technical efficiency score with 0-DF and 0.1-DF, and not a great value of sensitivity score with 0.1- DF among other DMUs. Therefore, 0.1-KAM suggests these DMUs as the best performers among remainder DMUs. 0.1-KAM also suggests DMUs ‘e’, ‘f’, ‘i! and ‘r’ as outliers, because there is a rapid difference between their technical efficiency scores with 0-DF and 0.1-DF.
Figure 4: Detecting best efficient DMUs by KAM. Khezrimotlagh, D. (2015). How to detect outliers in data envelopment analysis by Kourosh and Arash method. arXiv preprint arXiv: 1503.02548. The polygon chart of technical efficiency score with 0-DF is gradually decreased. As it depicted with two dotted vertical ellipses, DMUs ‘a’-‘d’, ‘g’ and ‘h’ have simultaneously a good value of technical efficiency score with 0-DF, a good value of best technical and lowest efficiency score with 0.1-DF, a lesser difference between technical efficiency score with 0-DF and 0.1-DF, and not a great value of sensitivity score with 0.1- DF among other DMUs. Therefore, 0.1-KAM suggests these DMUs as the best performers among remainder DMUs. 0.1-KAM also suggests DMUs ‘e’, ‘f’, ‘i! and ‘r’ as outliers, because there is a rapid difference between their technical efficiency scores with 0-DF and 0.1-DF.
We also applied KAM when ¢; and e;* were 0.5 X min{x;1: xj, # 0,i = 1,2, ...,100} and 0.5 xX min{y;1: viz # 0,i = 1,2,...,100}, respectively, and wy = 1/x,, and wf = 1/y,,. In this case, the effect on the Farrell frontier was the same for evaluated DMUs. There were no significant differences to arrange and benchmark DMUs. DMU ‘a’ still had the first rank, but it was suggested as an outlier due to have a very great sensitivity score by 0.5-DF. Moreover, the rank of technical efficient DMUs were respectively as ‘a’, ‘c’, ‘d’, ‘b’, ‘f and ‘e’. In order to have a clear figure, ¢; and ej were defined the same as 0.3 of unit and KAM was applied. Figure 7 depicts the 0.3-KAM benchmarks. From the figure, 0.3- KAM technical targets are between DMUs ‘a’ to ‘c’ on the Farrell frontier, which is the
We also applied KAM when ¢; and e;* were 0.5 X min{x;1: xj, # 0,i = 1,2, ...,100} and 0.5 xX min{y;1: viz # 0,i = 1,2,...,100}, respectively, and wy = 1/x,, and wf = 1/y,,. In this case, the effect on the Farrell frontier was the same for evaluated DMUs. There were no significant differences to arrange and benchmark DMUs. DMU ‘a’ still had the first rank, but it was suggested as an outlier due to have a very great sensitivity score by 0.5-DF. Moreover, the rank of technical efficient DMUs were respectively as ‘a’, ‘c’, ‘d’, ‘b’, ‘f and ‘e’. In order to have a clear figure, ¢; and ej were defined the same as 0.3 of unit and KAM was applied. Figure 7 depicts the 0.3-KAM benchmarks. From the figure, 0.3- KAM technical targets are between DMUs ‘a’ to ‘c’ on the Farrell frontier, which is the
Related topics:
Data Envelopment AnalysisOutlier detectionArash Method
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved