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Cross-correlation techniques provide a promising avenue for calibratingphotometric redshifts and determining redshift distributions using spectroscopywhich is systematically incomplete (e.g., current deep spectroscopic surveysfail to obtain secure redshifts for 30-50% or more of the galaxies targeted).In this paper we improve on the redshift distribution reconstruction methodspresented in Matthews & Newman (2010) by incorporating full covarianceinformation into our correlation function fits. Correlation functionmeasurements are strongly covariant between angular or spatial bins, andaccounting for this in fitting can yield substantial reduction in errors.However, frequently the covariance matrices used in these calculations aredetermined from a relatively small set (dozens rather than hundreds) ofsubsamples or mock catalogs, resulting in noisy covariance matrices whoseinversion is ill-conditioned and numerically unstable. We present here a methodof conditioning the covariance matrix known as ridge regression which resultsin a more well behaved inversion than other techniques common in large-scalestructure studies. We demonstrate that ridge regression significantly improvesthe determination of correlation function parameters. We then apply theseimproved techniques to the problem of reconstructing redshift distributions. Byincorporating full covariance information, applying ridge regression, andchanging the weighting of fields in obtaining average correlation functions, weobtain reductions in the mean redshift distribution reconstruction error of asmuch as ~40% compared to previous methods. In an appendix, we provide adescription of POWERFIT, an IDL code for performing power-law fits tocorrelation functions with ridge regression conditioning that we are makingpublicly available.

Improving Correlation Function Fitting with Ridge Regression: Application to Cross-Correlation Reconstruction