Tests for non-Gaussian statistics in the DMR four-year sky maps

We search the high-latitude portion of the COBE Differential Microwave Radiometer (DMR) 4 yr sky maps for evidence of a non-Gaussian temperature distribution in the cosmic microwave background. The genus, three-point correlation function, and two-point correlation function of temperature maxima and minima are all in excellent agreement with the hypothesis that the CMB anisotropy on angular scales of 7 degrees or larger represents a random-phase Gaussian field. A likelihood comparison of the DMR sky maps to a set of random-phase non-Gaussian toy models selects the exact Gaussian model as most likely. Monte Carlo simulations show that the two-point correlation of the peaks and valleys in the maps provides the greatest discrimination among the class of models tested.