Development and Evaluation of an Optimal Composite Estimator in Spatial Microsimulation Small Area Estimation

A range of data is of geographic interest but is not available at a small area level from existing data sources. Small area estimation (SAE) offers techniques to estimate population parameters of target variables to detailed scales based on relationships between those target variables and relevant auxiliary variables. The resulting indirect small area estimate can deliver a lower mean squared error compared to its direct survey estimate, given that variance can be reduced markedly even if bias increases. Spatial microsimulation SAE approaches are widely utilized but only beginning to engage with the potential of composite estimators that use a weighted combination of indirect and direct estimators to reduce further the mean squared error of the small area estimate compared to an indirect SAE estimator alone. This article advances these approaches by constructing for the first time in the microsimulation literature an optimal composite estimator for such SAE approaches in which the combining weight is calculated from the mean squared errors of the two estimators; thus, optimizing the reduction in MSE of the resulting small area estimates. This optimal composite estimator is demonstrated and evaluated in a model-based simulation study and application based on the real data.     

The distribution and sources of archaeological obsidian from southern France

One-hundred-and-sixty-two pieces of obsidian have been found at 50 archaeological localities in southern France. The distribution is concentrated in the Rhône Valley, but includes sites in Drôme and in southwest France. The obsidian is mainly from sites of the Chassey culture (4th and 3rd millennium Neolithic), but there is one Impressed Ware site (Early Neolithic) and four Copper Age sites with obsidian. Only a small proportion of the obsidian (31 pieces) consists of waste pieces, providing little evidence for on-site working. 10 pieces of obsidian were analysed by instrumental neutron activation analysis to determine their geological provenance. Seven pieces proved to be from the Sardinian SA source, one from Lipari, and two from Pantelleria. Chronologically there is some division between sources used: all three pieces of Liparian obsidian so far identified from southern France, in this work and by earlier researchers, belong to Early Chassey contexts, and the two Pantellerian pieces are from a Copper Age dolmen. Sardinian and Liparian obsidian probably reached France by way of northern Italy. where both types were in use in contemporary cultures. The two Pantellerian pieces are evidence of some type of contact between France and the southern Mediterranean in the Copper Age, despite earlier suggestions of a very restricted distribution for the Pantellerian source. Obsidian was probably imported to southern France with other goods since the small amounts used would not warrant a separate trading network for obsidian alone.