Combining a list and an area frame

The most widespread way to avoid instability of estimates and to improve their precision is to adopt a multiple-frame sample survey design. For agricultural surveys, a list of very large operators and of operators that produce rare items is combined with the area frame. If this list is short, it is generally easy to construct and update. A crucial aspect of this approach is the identification of the area sample units included in the list frame. When units in the area frame and in the list sample are not detected, the estimators of the population totals have an upward bias.

Sometimes a large and reliable list is available. In such cases the final estimates are essentially based on the list sample. The role of the area frame component in the multiple-frame approach is essentially solving the problems connected with incompleteness of the list and estimating the incompleteness of the list itself. In these cases, updating the list and record matching to detect overlapping sample units in the two frames are difficult and expensive operations that can produce relevant non-sampling errors (Vogel, 1975; Kott and Vogel, 1995).

Combining a list and an area frame is a special case of multiple-frame sample surveys in which sample units belonging to the lists and not to the area frame do not exist (domain b is empty) and the size of domain ab equals NB (frame B size: the list size, which is known).

This approach is very convenient when the list contains units with large (thus probably more variable) values of some variable of interest and the survey cost of units in the list is much lower than in the area frame (Kott and Vogel 1995; Carfagna, 2004). In fact, when A is an area frame, Yb in equation (3.2) is zero as well as cov(Yb, Yfb) in equations (3.3) and (3.4); thus, we have

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