  We propose a new statistical procedure able in some way to overcome the curse
of dimensionality without structural assumptions on the function to estimate.
It relies on a least-squares type penalized criterion and a new collection of
models built from hyperbolic biorthogonal wavelet bases. We study its
properties in a unifying intensity estimation framework, where an oracle-type
inequality and adaptation to mixed smoothness are shown to hold. Besides, we
describe an algorithm for implementing the estimator with a quite reasonable
complexity.
