The Hellinger distance between a nonparametric density estimator and a model family is minimized to produce estimates of location and covariance in multivariate data. With suitable restrictions on the density estimators and the model family, these minimum Hellinger distance estimators (MHDE's) are shown to be affine invariant, consistent, and asymptotically normal. The robustness of the MHDE as measured by the breakdown point compares favorably against the previously studiedM-estimators. Monte Carlo results suggest that the MHDE's are an attractive robust alternative to the usual sample means and covariance matrix.