Nonparametric estimation with quantized data

The accuracy lost to data quantization in the context of nonparametric density, regression and classification estimation problems is considered. We make use of quantization strategies which can be described by a certain auxiliary distribution (quantization density) function. The statistical accuracy of the resulting estimators is studied, i.e., we derive the pointwise and global L₂-distance results for the closeness of the estimators to both the true functions and the estimators based on the original unquantized data set