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Orthogonality conditions for convex regression
Sheng Dai, Timo Kuosmanen, Xun Zhou
https://arxiv.org/abs/2506.21110 https://arxiv.org…

Orthogonality conditions for convex regression
Econometric identification generally relies on orthogonality conditions, which usually state that the random error term is uncorrelated with the explanatory variables. In convex regression, the orthogonality conditions for identification are unknown. Applying Lagrangian duality theory, we establish the sample orthogonality conditions for convex regression, including additive and multiplicative formulations of the regression model, with and without monotonicity and homogeneity constraints. We th…