Speaker localization using microphone arrays is typically based on the expected phase and amplitude differences between microphones as a function of the wave arrival direction. However, in rooms with significant reverberation, the direct sound is contaminated by reflections and localization often fails. Recently, a reverberation-robust localization method was proposed, which uses only the direct-path bins in the short-time Fourier transform (STFT) of the speech signals. The method is based on thresholding according to the ratio between the first two singular values of the spatial spectrum matrix. In this work, a confidence measure is developed based on this ratio, which is then used for speaker localization in a statistical estimation framework, based on a Gaussian mixture model. The paper presents the theory of the proposed method and simulation examples validating the advantages of the new approach.