Limiting distributions under random or non-product fixed designs

Establish limiting distributions for least squares estimators in additive monotone models under random designs or non-product fixed designs.

Background

The paper’s principal asymptotic theory relies on a Cartesian-product fixed lattice, which decouples the componentwise estimators. Under random designs, this decoupling fails, and the existing oracle-property argument depends on a uniform boundedness claim for the least squares estimators whose complete proof is unavailable.

The authors therefore leave the extension of limiting-distribution theory to random and non-product fixed designs unresolved.