Theory of Probability and Mathematical Statistics
Characterization of the least squares estimator: Mis-specified multivariate isotonic regression model with dependent errors
Pramita Bagchi and Subhra Sankar Dhar
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Abstract: 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.
Keywords: Hilbert space, optimization problem, projection
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