Pairwise Estimating Equations for the Analysis of Linked Data

In official statistics record linkage is an important activity, which consists in identifying records from the same individual in one or many files.It is used to combine data sources including admistrative, survey or big data sources.In practice, record linkage is subject to linkage errors when it relies on quasi-identifiers, such as names and demographic variables, which are nonunique and recorded with errors.Accounting for these errors is an important but challenging problem.In this work, two methods are described for the primary analysis of such data, i.e. an analysis by someone with unfettered access to all the related micro-data and project information.Both solu-B records are indexed over a subset B ⊂ {1, . . ., N }, where |B| is possibly different from |A|.We are interested in situations where the two files overlap significantly, i.e., where the ratio |A ∩ B| / min (|A|, |B|) is sufficiently large 1 .In the Cartesian product A * × B * , consider the pair (i, j) and define m ij and γ ij , the pair match status and comparison vector, respectively.Let M = [m ij ] 1≤i,j≤N denote the match matrix in A * × B * .In B * , let z j denote the observed responses from record j in B * , and define the vector z = z 1 . . .z N .As before, let X = x 1 . . .x N denote the matrix of all the covariates in register A * .Finally let y = y 1 . . .y N denote the actual responses, where y i is the actual response for record i in A * .As before, the finite population comprises of H IID blocks that each contain a variable but bounded number of IID individuals.Block h has size N h , where N h ≤ C for some constant C that does not depend on H, with N = N 1 + . . .+ N H .The block also corresponds to records indexed in the subsets A * h and B * h in the files A * and B * respectively, where |A * h | = |B * h | = N h .Let A h and B h denote the corresponding subsets in files A and B respectively, and let M h denote the match matrix in A * h × B * h ; the Cartesian product within the block. AssumptionsThe following assumptions are made that extend those of Section 3.3.A.1 The match matrix M h is a uniform random permutation independent of [x i ] i∈A * h .A.2 For i ∈ A * h , let j(i) denote the index of the corresponding record in B * h .The variables [y i ] i∈A * h , [I (j(i) ∈ B h )] i∈A * h , [I (i ∈ A h )] i∈A * h , M h , and {γ ij } (i,j)∈A * h ×B * h are conditionally mutually independent given the block size N h and the covariates [x i ] i∈A * h .1 When the overlap is small, statistical matching may be a better solution.where q ij is given by Eq. (4.1).Proof: Consider (i, j) ∈ A * h × B * h .As before, we have g (z j , x i ) =

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