By Ruey S. Tsay
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Extra resources for Analysis of Financial Time Series (Wiley Series in Probability and Statistics - Applied Probability and Statistics Section Series)
L1 Evidently the following two statements are equivalent: 1. 2. A DMU is efficient if and only if the following two conditions are satisfied: (a) ()* = 1; ( b) all slacks are zero. A DMU is efficient if and only if w~ = z~ = 1. 'The nonzero slacks and the value of ()* ~ 1 identify the sources and amount of any inefficiencies that may be present. Figure 2-5 illustrates the situation for the example DMUs of figure 2-1. In an input orientation, the objective is to produce the observed outputs with a minimum resource level.
American Economic Review (1992), 82(2):428-433. Lovell, C. A. , Wood, L. Stratified Models of Education Production Using Modified DEA and Regression Analysis. Chapter 17, this book. , Stoker, B. Data Envelopment Analysis: The Assessment of Performance. New York: John Wiley & Sons (1991). INTRODUCTION 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 21 Pareto, V. Manuel d'economie politique, 2nd ed. Paris: Marcer! Giard (1927). Petersen, N. C. Data Envelopment Analysis on a Relaxed Set of Assumptions.
P6 0L---~2----~4----~6----~8----1~0--~12X Figure 2-5. Table 2-2. Envelopment surface for the BCC-Input model. Solution Values for the Input-Oriented BCC Model Primal Problem (BCCp-I) DMU ()* s+ 1 1 1 0 0 0 0 0 2 3 4 5 6 7 1 1 7115 1/2 3/5 1 0 s 0 0 0 0 0 0 0 Dual Problem (BBCD-I) A w~ J f1 v uo Al = 1 A2 = 1 A3 = 1 A4 = 1 Al = 2/3, A2 = 113 Al = 1 A3 = 1 1 1 1/6 1/3 114 113 1/15 e 3/20 112 113 116 119 115 1/4 1/10 2/3 -2/3 -3/4 -5/3 4/15 ! -e 3/5 efficiency as given above fails to be satisfied.
Analysis of Financial Time Series (Wiley Series in Probability and Statistics - Applied Probability and Statistics Section Series) by Ruey S. Tsay