7,227 research outputs found

    Nonparametric Productivity Analysis

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    How can we measure and compare the relative performance of production units? If input and output variables are one dimensional, then the simplest way is to compute efficiency by calculating and comparing the ratio of output and input for each production unit. This idea is inappropriate though, when multiple inputs or multiple outputs are observed. Consider a bank, for example, with three branches A, B, and C. The branches take the number of staff as the input, and measures outputs such as the number of transactions on personal and business accounts. Assume that the following statistics are observed: Branch A: 60000 personal transactions, 50000 business transactions, 25 people on staff, Branch B: 50000 personal transactions, 25000 business transactions, 15 people on staff, Branch C: 45000 personal transactions, 15000 business transactions, 10 people on staff. We observe that Branch C performed best in terms of personal transactions per staff, whereas Branch A has the highest ratio of business transactions per staff. By contrast Branch B performed better than Branch A in terms of personal transactions per staff, and better than Branch C in terms of business transactions per staff. How can we compare these business units in a fair way? Moreover, can we possibly create a virtual branch that reflects the input/output mechanism and thus creates a scale for the real branches? Productivity analysis provides a systematic approach to these problems. We review the basic concepts of productivity analysis and two popular methods DEA and FDH, which are given in Sections 12.1 and 12.2, respectively. Sections 12.3 and 12.4 contain illustrative examples with real data.relative performance, production units, productivity analysis, Data Envelopment Analysis, DEA, Free Disposal Hull, DFH, insurance agencies, manufacturing industry

    Limit Distribution of Convex-Hull Estimators of Boundaries

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    Given n independent and identically distributed observations in a set G with an unknown function g, called a boundary or frontier, it is desired to estimate g from the observations. The problem has several important applications including classification and cluster analysis, and is closely related to edge estimation in image reconstruction. It is particularly important in econometrics. The convex-hull estimator of a boundary or frontier is very popular in econometrics, where it is a cornerstone of a method known as `data envelope analysis´ or DEA. In this paper we give a large sample approximation of the distribution of the convex-hull estimator in the general case where p>=1. We discuss ways of using the large sample approximation to correct the bias of the convex-hull and the DEA estimators and to construct confidence intervals for the true function. --Convex-hull,free disposal hull,frontier function,data envelope analysis,productivity analysis,rate of convergence

    Asymptotic distribution of conical-hull estimators of directional edges

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    Nonparametric data envelopment analysis (DEA) estimators have been widely applied in analysis of productive efficiency. Typically they are defined in terms of convex-hulls of the observed combinations of inputs×outputs\mathrm{inputs}\times\mathrm{outputs} in a sample of enterprises. The shape of the convex-hull relies on a hypothesis on the shape of the technology, defined as the boundary of the set of technically attainable points in the inputs×outputs\mathrm{inputs}\times\mathrm{outputs} space. So far, only the statistical properties of the smallest convex polyhedron enveloping the data points has been considered which corresponds to a situation where the technology presents variable returns-to-scale (VRS). This paper analyzes the case where the most common constant returns-to-scale (CRS) hypothesis is assumed. Here the DEA is defined as the smallest conical-hull with vertex at the origin enveloping the cloud of observed points. In this paper we determine the asymptotic properties of this estimator, showing that the rate of convergence is better than for the VRS estimator. We derive also its asymptotic sampling distribution with a practical way to simulate it. This allows to define a bias-corrected estimator and to build confidence intervals for the frontier. We compare in a simulated example the bias-corrected estimator with the original conical-hull estimator and show its superiority in terms of median squared error.Comment: Published in at http://dx.doi.org/10.1214/09-AOS746 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    UV-LIGA micro-fabrication of inertia type electrostatic transducers and their application

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    This dissertation discusses the design, working principles, static & dynamic analysis and simulation, mechanics of material, applied MEMS technology, micro-fabrication, and experimental testing of two types of micro-transducers: micro-power relay and micro-accelerometer. Several possible design concepts were proposed, and the advantages and disadvantages of electrostatic working principles were also discussed. Transducers presented in this research used electrostatic force as a driving force in the micro-relay and capacitance as a sensing parameter in the micro-accelerometer. There was an analogy between the micro-relay and the micro-accelerometer in their theoretical approach and fabrication processes. The proposed micro-transducers (micro-relay and micro-accelerometer) were fabricated using UV lithograph of SU-8 & SPR and UV-LIGA process. The advantages and disadvantages of these processes were discussed. The micro-relays fabricated by UV-LIGA technology had the following advantages compared with other reported relays: fast switching speed, high power capacity, high off-resistance, lower on-resistance, low power consumption, and low heat generation. The polymer-based micro-accelerometers were designed and fabricated. Instead of applying SU-8 only as a photo resist, cured SU-8 was used as the primary structural material in fabricating the micro-accelerometers. The great flexibility in size and aspect ratio of cured SU-8 made it feasible to produce highly sensitive accelerometers. The prototype micro-relays and micro-accelerometers were tested for the dynamic characteristics and power capacity. The experimental results in micro-relays had confirmed that reasonably large current capacity and fast response speed was able to be achieved using electromagnetic actuation and the multilayer UV-LIGA fabrication process

    Monomial Relization of Crystal Bases for Special Linear Lie Algebras

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    We give a new realization of crystal bases for finite dimensional irreducible modules over special linear Lie algebras using the monomials introduced by H. Nakajima. We also discuss the connection between this monomial realization and the tableau realization given by Kashiwara and Nakashima.Comment: 15 page
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