Characterization of the least squares estimator: Mis-specified multivariate isotonic regression model with dependent errors

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 \beta -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.