  The problem of joint universal source coding and modeling, addressed by
Rissanen in the context of lossless codes, is generalized to fixed-rate lossy
coding of continuous-alphabet memoryless sources. We show that, for bounded
distortion measures, any compactly parametrized family of i.i.d. real vector
sources with absolutely continuous marginals (satisfying appropriate smoothness
and Vapnik--Chervonenkis learnability conditions) admits a joint scheme for
universal lossy block coding and parameter estimation, and give nonasymptotic
estimates of convergence rates for distortion redundancies and variational
distances between the active source and the estimated source. We also present
explicit examples of parametric sources admitting such joint universal
compression and modeling schemes.
