Variance estimation with matched pairs

Abstract

We wish to estimate the variance σ 2 from n pairs ( X i ,Y i ) which are independent normal random variables with unknown mean μ i and variance σ 2 . According to a marginal or conditional sufficiency argument, all useful information about σ 2 is contained in the differences X i − Y i . This paper shows that under fairly weak assumptions about the means, a considerable amount of information is also extractable from the sums X i + Y i .