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This article investigates some nice properties of the least squares estimator of multivariate isotonic regression function (denoted as LSEMIR), when the model is mis-specified, and the errors are β -mixing stationary random variables. Under mild conditions, it is observed that the least squares estimator converges uniformly to a certain monotone function, which is closest to the original function in an appropriate sense.
Bagchi et al. (Fri,) studied this question.