The genetic contribution of a parental population in an admixed population can be estimated from the frequencies of unique alleles that exist only in that parental population. In this work we show that although the estimated admixture component from a single such unique allele may be quite unstable, when multiple numbers of unique alleles are recognized, they together allow precise estimation of admixture components in an admixed population. We develop a statistical theory of linear regression incorporating estimation errors of frequencies of unique alleles in the parental and admixed populations. In addition, we show that the distribution of unique alleles detected in individuals can be used to measure the admixture component of an admixed individual. Applications of these theories to data on unique African alleles in an American black population show that such estimates are quite reliable. The distribution of unique alleles detected from the multiple-locus genotype of an admixed individual allows an opportunity to extend the studies on the "hereditary" basis of disease risk variation across populations to individuals from a single homogeneous admixed population.