不完全了解输入和输出值的数据包络分析模型：在葡萄牙公立医院的应用
Data Envelopment Analysis models with imperfect knowledge of input and output values: An application to Portuguese public hospitals
摘要：
要评估一组观测的技术效率，就需要完全了解由投入和产出组成的相关数据。如果不是这种情况，则可能会得到有偏估计。数据包络分析（DEA）是一种最广泛使用的数学模型来估计效率。它构造了一个分段线性边界，所有观测值都与之进行比较。由于边界是根据经验定义的，因此由低数据质量（数据知识或IKD不完善）导致的任何偏差都可能导致效率低估/高估。在这项研究中，我们模型IKD，然后，应用所谓的打\&运行过程随机生成可接受的意见，一些预先指定的概率密度函数。用于对IKD建模的集限制了与每个观测相关联的数据域。属于该域的任何点都可以作为效率评估的观察点。因此，这个采样过程必须运行相当多的次数（理论上是无限次），以填充整个集合。在每次迭代的执行过程中使用DEA技术来估计每次观察的自举效率得分。我们使用一些场景来表明，建议的例程可以优于一些可用的替代品。我们还解释了如何效率估计可以用于统计推断。基于葡萄牙公立医院数据库（2013-2016）的实证案例研究，解决了使用所提出的方法。
英文摘要：
Assessing the technical efficiency of a set of observations requires that the associated data composed of inputs and outputs are perfectly known. If this is not the case, then biased estimates will likely be obtained. Data Envelopment Analysis (DEA) is one of the most extensively used mathematical models to estimate efficiency. It constructs a piecewise linear frontier against which all observations are compared. Since the frontier is empirically defined, any deviation resulting from low data quality (imperfect knowledge of data or IKD) may lead to efficiency under/overestimation. In this study, we model IKD and, then, apply the so-called Hit \& Run procedure to randomly generate admissible observations, following some prespecified probability density functions. Sets used to model IKD limit the domain of data associated with each observation. Any point belonging to that domain is a candidate to figure out as the observation for efficiency assessment. Hence, this sampling procedure must run a sizable number of times (infinite, in theory) in such a way that it populates the whole sets. The DEA technique is used during the execution of each iteration to estimate bootstrapped efficiency scores for each observation. We use some scenarios to show that the proposed routine can outperform some of the available alternatives. We also explain how efficiency estimations can be used for statistical inference. An empirical case study based on the Portuguese public hospitals database (2013-2016) was addressed using the proposed method.
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