  Purchase data from retail chains provide proxy measures of private household
expenditure on items that are the most troublesome to collect in the
traditional expenditure survey. Due to the sheer amount of proxy data, the bias
due to coverage and selection errors completely dominates the variance. We
develop tests for bias based on audit sampling, which makes use of available
survey data that cannot be linked to the proxy data source at the individual
level. However, audit sampling fails to yield a meaningful mean squared error
estimate, because the sampling variance is too large compared to the bias of
the big data estimate. We propose a novel accuracy measure that is applicable
in such situations. This can provide a necessary part of the statistical
argument for the uptake of big data source, in replacement of traditional
survey sampling. An application to disaggregated food price index is used to
demonstrate the proposed approach.
