  We obtain estimates relating the phase space and the parameter space of
analytic families of unimodal maps. Using those estimates, we show that typical
analytic unimodal maps admit a quasiquadratic renormalization. This reduces the
study of the statistical properties of typical unimodal maps to the
quasiquadratic case which had been studied in \cite {AM2}. The estimates proved
here correspond exactly to the Phase-Parameter relation proved in \cite {AM} in
the quadratic case, and allows one to obtain sharp estimates on the dynamics of
typical unimodal maps which were available only in the quadratic case: as an
example we conclude that the exponent of the polynomial recurrence of the
critical orbit is exactly one. We also show that those ideas lead to a new
proof of a Theorem of Shishikura: the set of non-renormalizable parameters in
the boundary of the Mandelbrot set has Lebesgue measure zero. Further
applications of those results can be found in the companion paper \cite {AM3}.
