The effect of errors in variables in quantization is investigated. We prove
general exact and non-exact oracle inequalities with fast rates for an
empirical minimization based on a noisy sample
Zi=Xi+ϵi,i=1,…,n, where Xi are i.i.d. with density f and
ϵi are i.i.d. with density η. These rates depend on the geometry
of the density f and the asymptotic behaviour of the characteristic function
of η.
This general study can be applied to the problem of k-means clustering with
noisy data. For this purpose, we introduce a deconvolution k-means stochastic
minimization which reaches fast rates of convergence under standard Pollard's
regularity assumptions.Comment: 30 pages. arXiv admin note: text overlap with arXiv:1205.141