Estimating α-frontier technical efficiency with shape-restricted kernel quantile regression

摘要: In frontier analysis, most of nonparametric approaches produce a full that envelopes all observations. Its sensitivity to extreme values and outliers can be overcome by @a-frontier, which is defined as the @a-quantile output conditional on given input. The @a-frontier regarded benchmark whether specified firm achieves top @a efficiency. This paper proposes smooth multivariate estimation for based shape-restricted kernel quantile regression. method explicitly appends classical regression with two shape restrictions: nondecreasing concave, are necessary conditions production functions. training semi-infinite programming discretized semidefinite problem, computationally tractable. Theoretical analysis shows rate exceedance in samples will converge size data increases. Experimental results toy sets clearly show this exploitation these prior knowledge greatly improve learning performance. set from NBER-CES Manufacturing Industry Database shaped restricted achieve better out-of-sample performance than those methods.