We consider the rate of convergence of the expected loss of empirically
optimal vector quantizers. Earlier results show that the mean-squared expected
distortion for any fixed distribution supported on a bounded set and satisfying
some regularity conditions decreases at the rate O(log n/n). We prove that this
rate is actually O(1/n). Although these conditions are hard to check, we show
that well-polarized distributions with continuous densities supported on a
bounded set are included in the scope of this result.Comment: 18 page
