This article is concerned with the file linkage problem first investigated
by DeGroot and Goel (1980). Let X-1,..., X-n be a random sample from a biva
riate normal distribution. Suppose that before the sample can be observed,
it is broken into the components and X-1,X-1,..., X-1,X-n and X-2,X-psi (1)
,..., X-2,X-psi (n) where X-j = (X-1,X-j, X-2,X-j)' and psi is some unknown
permutation of The aim is to estimate the parameters (in particular the co
rrelation coefficient) of the bivariate normal distribution using the above
broken random sample. The main difficulty here is that direct computation
of the likelihood is in general a NP-hard problem. Thus for n sufficiently
large, standard likelihood or Bayesian techniques may not be feasible. This
article proposes to reformulate the problem as a moment problem via Fisher
's k-statistics. The resulting likelihood can be approximated as a product
of bivariate normal likelihoods and consequently standard statistical metho
ds can be applied. It is also shown that this approximation is very good in
that very little Fisher information is lost.