Indirect sampling Clause Samples

Indirect sampling. Indirect sampling starts from a sample s of ns units obtained with a probability sampling design, it enlarges the initial sample using a link matrix and it associates estimation weights to the final sample units using the initial sampling weights and the link matrix. The sampling strategy is based on the Generalized Weight Share Method (GWSM – ▇▇▇▇▇▇▇▇, 1995; 2002; ▇▇▇▇▇▇▇ and ▇▇▇▇▇▇▇▇, 2006) that can be viewed as a generalization of Network Sampling and also of Adaptive Cluster Sampling (▇▇▇▇▇▇▇▇, 1992; ▇▇▇▇▇▇▇▇ and ▇▇▇▇▇, 1996). The objective is the estimation of a set of parameters of the RA and JC population using the PI-Silc sampling weights and the link matrix generated by the matching procedure (see § 4). The set of individuals selected and surveyed by ▇▇-▇▇▇▇ is considered a random sample s of size ns . For each unit in the sample the set of units is defined on the result of the record linkage process between the Pi-Silc data and the JC (RA) datasets. Let indicate this additional set with c of size nc . In such way the initial sample of PI-Silc units is enlarged adding the linked units in the JC (RA) data. The correspondence between the sampled unit and the unit in the administrative data set can be W = ⎡wsc ⎤ s c represented by a link matrix wsc ≥ 0 ji ⎦ of size n × n where each element the linkage weight wsc > 0 ji . That is, unit j of s is related to unit i of c provided that ji , otherwise the two units are not related to each other. We assume that for any unit j the values of the link matrix can be obtained. Notice that in this application only one unit j has been finally selected for each sampled unit i. As a consequence the size of the target populations (JC/RA) is the same as the size of Pi-Silc sample. W = W ⎡diag(1T W )⎤−1 The link matrix can be also defined in standardized form sc