ارزیابی خارج از نمونه برای DEA با کاربرد آن در پیش بینی ورشکستگی An out-of-sample evaluation framework for DEA with application in bankruptcy prediction

1 Introduction Since the publication of the seminal paper by Charnes, Cooper and Rhodes in 1978, Data envelopment analysis (DEA) has become a well-established non-parametric methodology for performance evaluation and benchmarking. DEA has witnessed a widespread use in many application areas—see Liu et al. (2013) for a recent survey, and Mousavi et al. (2015) and Xu and Ouenniche (2011, 2012a, b) for a recent application area—along with many methodological contributions—see, for example,Banker et al.(1984), Andersen and Petersen (1993), Tone (2001, 2002) and Seiford and Zhu (2003). Despite the growing use of DEA, to the best of our knowledge, no published work formally addressed out-of-sample evaluation in DEA. In this paper, we fill this gap by proposing a framework for the out-of-sample evaluation of decision making units. We illustrate the use of the proposed framework in bankruptcy prediction of companies listed on the London Stock Exchange. Note that prediction of risk class or bankruptcy is one of the major activities in auditing firms’ risks and uncertainties. The design of reliable models to predict bankruptcy is crucial for many decision making processes. Bankruptcy prediction models could be divided into two broad categories depending on whether they are static (see, for example, Altman 1968, 1983; Taffler 1984; Theodossiou 1991; Ohlson 1980; Zmijewski 1984) or dynamic (see, for example, Shumway 2001; Bharath and Shumway 2008; Hillegeist et al. 2004). In this paper we shall focus on the first category of models to illustrate how outof-sample evaluation of companies could be performed. The most popular static bankruptcy prediction models are based on statistical methodologies (e.g., Altman 1968, 1983; Taffler 1984), stochastic methodologies (e.g., Theodossiou 1991; Ohlson 1980; Zmijewski 1984), and artificial intelligence methodologies (e.g., Kim and Han 2003; Li and Sun 2011; Zhang et al. 1999; Shin et al. 2005). DEA methodologies are increasingly gaining popularity in bankruptcy prediction (e.g., Cielen et al. 2004; Paradi et al. 2004; Premachandra et al. 2011; Shetty et al. 2012). However, the issue of out-of-sample evaluation remains to be addressed when DEA is used as a classifier. The remainder of this paper is organised as follows. In Sect. 2, we propose a formal framework for performing out-of-sample evaluation in DEA. In Sect. 3, we provide information on the bankruptcy data we used along with details on the design of our experiment, and present our empirical findings. Finally, Sect. 4 concludes the paper.