“…As shown in Table 1, the nonparametric quantile-like estimators can also be classified into convex and nonconvex estimators depending on whether the assumption of convexity is imposed on the production possibility set. Under relaxed convexity assumptions, order-α is a representative nonconvex partial frontier estimator, which has been extensively applied in frontier estimation and performance evaluation (see, e.g., Wheelock & Wilson, 2008;Wheelock & Wilson, 2009;Matallín-Sáez et al, 2019;Kounetas et al, 2021). In sharp contrast, there are no nonconvex quantile estimators existing in the literature.…”