Nonparametric estimation of the regression function from quantized observations

The problem of estimating the regression function for a fixed design model is considered when only quantized and correlated data are available. Moreover, repeated observations are required in order for the constructed estimator to be consistent. The asymptotic performance in terms of the mean squared error for the regression function estimator constructed from quantized observations is derived. The generated optimal bandwidth depends on the regularity of the process, the number of replications, and the number of levels of quantization. The behavior and the comparison of the performances between quantized and plain estimators are investigated through some examples.