Enhancing data envelopment analysis: a comprehensive calibration with random forests

Table 3 Monte Carlo results: MSE of scenarios with 5 redundant inputs

n	P	RF-DEA	DEA	Imp\(\%\)	RF-DEA	DEA	Imp\(\%\)
n	P	Q = 1			Q = 2
n = 50	P = 2	0.030 (0.008)	0.035 (0.007)	14.42%	0.028 (0.009)	0.038 (0.007)	25.90%
n = 50	P = 3	0.032 (0.007)	0.039 (0.006)	16.12%	0.028 (0.009)	0.040 (0.007)	30.12%
n = 100	P = 2	0.026 (0.006)	0.031 (0.004)	18.00%	0.027 (0.006)	0.034 (0.005)	21.79%
n = 100	P = 3	0.031 (0.006)	0.036 (0.004)	13.76%	0.026 (0.007)	0.038 (0.005)	31.62%
n = 200	P = 2	0.021 (0.005)	0.026 (0.003)	17.20%	0.025 (0.005)	0.030 (0.003)	15.13%
n = 200	P = 3	0.027 (0.005)	0.031 (0.004)	10.41%	0.026 (0.006)	0.034 (0.003)	22.19%
n = 400	P = 2	0.019 (0.004)	0.021 (0.002)	10.72%	0.023 (0.005)	0.025 (0.002)	7.40%
n = 400	P = 3	0.023 (0.003)	0.026 (0.002)	12.54%	0.025 (0.007)	0.030 (0.002)	16.09%

Notes: Imp\(\%\): Improvement in performance (e.g., \(1-\text {MSE}_{\text {RF-DEA}}/\text {MSE}_{\text {DEA}}\))
Standard deviation in parentheses
Number of replications = 100, VRS assumption