  The problem of joint universal source coding and identification is considered
in the setting of fixed-rate lossy coding of continuous-alphabet memoryless
sources. For a wide class of bounded distortion measures, it is shown that any
compactly parametrized family of $\R^d$-valued i.i.d. sources with absolutely
continuous distributions satisfying appropriate smoothness and
Vapnik--Chervonenkis learnability conditions, admits a joint scheme for
universal lossy block coding and parameter estimation, such that when the block
length $n$ tends to infinity, the overhead per-letter rate and the distortion
redundancies converge to zero as $O(n^{-1}\log n)$ and $O(\sqrt{n^{-1}\log
n})$, respectively. Moreover, the active source can be determined at the
decoder up to a ball of radius $O(\sqrt{n^{-1} \log n})$ in variational
distance, asymptotically almost surely. The system has finite memory length
equal to the block length, and can be thought of as blockwise application of a
time-invariant nonlinear filter with initial conditions determined from the
previous block. Comparisons are presented with several existing schemes for
universal vector quantization, which do not include parameter estimation
explicitly, and an extension to unbounded distortion measures is outlined.
Finally, finite mixture classes and exponential families are given as explicit
examples of parametric sources admitting joint universal compression and
modeling schemes of the kind studied here.
