REPLICATE VARIANCE ESTIMATION USING PERMANENT REPLICATE INDENTIFIERS
The transformed ABS output estimation capability will provide variances using a replication approach. There is little change to current methods for replicate variance estimation, except that they will be supported by a permanent set of replicate identifiers for each survey unit, rather than replicates being generated at the time of variance estimation. This approach simplifies the correct estimation of variances based on multiple time points and will allow for integrated outputs based on multiple surveys.
Most ABS household and business surveys are conducted using complex survey designs and many produce statistics that are complex functions of elementary estimates (e.g. ratios, differences of ratios). Re-sampling methods have been chosen as the preferred method of variance estimation for ABS household and business surveys , since the alternative linearisation method can be quite cumbersome to implement for complex survey designs, as it requires the derivation of separate variance formulae for each non-linear estimator.
In ABS business surveys the current variance estimation method used is the without replacement rescaled bootstrap procedure (Chipperfield and Preston, 2007), while in ABS household surveys the primary variance estimation method used is the delete-a-group jackknife method (Kott, 1998). While the bootstrap procedure is still considered the most suitable method of replicate variance estimation for ABS business surveys, the current application of the rescaled bootstrap procedure has several less than ideal properties, including the requirement for multiple sets of replicate identifiers for various situations and the underestimation of the movement variances in particular situations.
An alternative application of the rescaled bootstrap procedure is that it will use a permanent set of replicate identifiers over time and across surveys. This permanent set of replicate identifiers will be generated from sets of replicate identifiers for a fixed number of replicate groups, since it will be more efficient from an operational perspective. The alternative application of the rescaled bootstrap procedure will overcome the issues associated with the current application of the rescaled bootstrap procedure.
The permanent sets of replicate identifiers for the fixed number of replicate groups in the bootstrap procedure will be generated from a Hadamard matrix H of order 256 to yield first-order and second-order balance. The scaled bootstrap weight method (Saavedra, 2001; Beaumont and Patak, 2012) will be incorporated into the bootstrap procedure to avoid negative bootstrap weights.
The delete-a-group jackknife method will also use permanent sets of replicate identifiers. One permanent set of replicates will be attached to Base Frame Units (BFU) on the area based private dwelling frame, and to dwellings on a list based non-private dwelling frame. Another permanent set of replicates will be attached to dwellings on the ABS address register.
Further Information
For more information, please contact John Preston (07) 3222 6229 or john.preston@abs.gov.au.
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