  We study the sequential calibration of estimations in a quantized isotonic L2
regression setting. We start by showing that the optimal calibrated quantized
estimations can be acquired from the traditional isotonic L2 regression
solution. We modify the traditional PAVA algorithm to create calibrators for
both batch and sequential optimization of the quantized isotonic regression
problem. Our algorithm can update the optimal quantized monotone mapping for
the samples observed so far in linear space and logarithmic time per new
unordered sample.
