Correlations in the spatial power spectra inferred from angular clustering: Methods and application to the automated plate measuring survey

We reconsider the inference of spatial power spectra from angular clustering data and show how to include correlations in both the angular correlation function and the spatial power spectrum. Inclusion of the full covariance matrices loosens the constraints on large-scale structure inferred from the Automated Plate Measuring (APM) survey by over a factor of 2. We present a new inversion technique based on singular-value decomposition that allows one to propagate the covariance matrix on the angular correlation function through to that of the spatial power spectrum and to reconstruct smooth power spectra without underestimating the errors. Within a parameter space of the cold dark matter (CDM) shape Gamma and the amplitude sigma (8), we find that the angular correlations in the APM survey constrain Gamma to be 0.19-0.37 at 68% confidence when fitted to scales larger than k = 0.2 h Mpc(-1). A downturn in power at k < 0.04 h Mpc(-1) is significant at only 1 <sigma>. These results are optimistic, since we include only Gaussian statistical errors and neglect any boundary effects.