A statistical analysis of adaptive quantization based on causal past

A statistical estimation framework is proposed for adaptive quantization based on causal past. Different estimation methods are given for the marginal density based on the quantized sample. For a stationary and ergodic source process, if its marginal density is in a parametric family with a dimension less than the quantization level, then “adaptation” can be achieved when the sample size is large, i.e., the marginal density can be estimated consistently