This paper presents a nonparametric technique of speaker recognition and verification. Some statistics and their distance measures of speech are evaluated for short utterances. The proposed distance measures are different from existing ones in their straightforward symmetricity. The computational efficiency and effectiveness in performance are demonstrated by a set of experiments. A new cohort selection is proposed and a 99.6% verification rate is reported on a database of 200 French speakers. From a nonparametric viewpoint, the facts are revealed that the statistics of covariance carries more speaker information than the sample mean, short term dynamics of speech is also of important speaker discriminative characteristics.