The Consistency ot the Empirical Quantization Error

2024/01/18 by Pötzelberger, Klaus

paper · doi:10.57938/0aed3f0a-bb25-4e05-a0e4-1d3b0a44fa74

Abstract

We study the empirical quantization error in case the number of prototypes increases with the size of the sample. We present a proof of the consistency of the empirical quantization error and of corresponding estimators of the quantization dimensions of distributions. (author's abstract)

Related

• The Quantization Dimension of Distributions
• Constructive quantization: approximation by empirical measures
• The General Quantization Problem for Distributions with Regular Support
• Sampling errors of quantile estimations from finite samples of data
• Optimality of empirical measures as quantizers