A Model-Independent Photometric Redshift Estimator

We derive a simple empirical photometric redshift estimator using a training set of galaxies with multiband photometry and measured redshifts in the Hubble Deep Field (HDF). This estimator is model-independent; it does not use spectral templates. The dispersion between the estimated redshifts and the spectroscopically measured ones is small; the dispersions range from $\sigma_z\simeq 0.03$ to 0.1 for $z\la 2$ galaxies, and from $\sigma_z\simeq 0.14$ to 0.25 for $z\ga 2$ galaxies. The predictions provided by our empirical redshift estimator agree well with recently measured galaxy redshifts. We illustrate how our empirical redshift estimator can be modified to include flat spectrum galaxies with $1.4\la z \la 2$.