  We use a Quadratic Maximum Likelihood (QML) method to estimate the angular
power spectrum of the cross-correlation between cosmic microwave background and
large scale structure maps as well as their individual auto-spectra. We
describe our implementation of this method and demonstrate its accuracy on
simulated maps. We apply this optimal estimator to WMAP 7-year and NRAO VLA Sky
Survey (NVSS) data and explore the robustness of the angular power spectrum
estimates obtained by the QML method. With the correction of the declination
systematics in NVSS, we can safely use most of the information contained in
this survey. We then make use of the angular power spectrum estimates obtained
by the QML method to derive constraints on the dark energy critical density in
a flat $\Lambda$CDM model by different likelihood prescriptions. When using
just the cross-correlation between WMAP 7 year and NVSS maps with 1.8$^\circ$
resolution, the best-fit model has a cosmological constant of approximatively
70% of the total energy density, disfavouring an Einstein-de Sitter Universe at
more than 2 $\sigma$ CL (confidence level).
