  We generalize the Jeffrey-Kirwan localization theorem for non-compact
symplectic and hyperKahler quotients. Similarly to the circle compact
integration of Hausel and Proudfoot we define equivariant integrals on
non-compact manifolds using the Atiyah-Bott-Berline-Vergne localization formula
as formal definition. We introduce a so called equivariant Jeffrey-Kirwan
residue and we show that it shares similar properties as the usual one. Our
localization formula has the same structure as the usual Jeffrey-Kirwan
formula, but it uses formal integration and equivariant residue. We also give a
version for hyperKahler quotients. Finally, we apply our formula to compute the
equivariant cohomology ring of Hilbert scheme of points on the plane
constructed as a hyperKahler quotient.
