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March 2013 Geostatistical modeling in the presence of interaction between the measuring instruments, with an application to the estimation of spatial market potentials
Francesco Finazzi
Ann. Appl. Stat. 7(1): 81-101 (March 2013). DOI: 10.1214/12-AOAS588

Abstract

This paper addresses the problem of recovering the spatial market potential of a retail product from spatially distributed sales data. In order to tackle the problem in a general way, the concept of spatial potential is introduced. The potential is concurrently measured at different spatial locations and the measurements are analyzed in order to recover the spatial potential. The measuring instruments used to collect the data interact with each other, that is, the measurement at a given spatial location is affected by the concurrent measurements at other locations. An approach based on a novel geostatistical model is developed. In particular, the model is able to handle both the measuring instrument interaction and the missing data. A model estimation procedure based on the expectation–maximization algorithm is provided as well as standard inferential tools. The model is applied to the estimation of the spatial market potential of a newspaper for the city of Bergamo, Italy. The estimated spatial market potential is eventually analyzed in order to identify the areas with the highest potential, to identify the areas where it is profitable to open additional newsstands and to evaluate the newspaper total market volume of the city.

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Francesco Finazzi. "Geostatistical modeling in the presence of interaction between the measuring instruments, with an application to the estimation of spatial market potentials." Ann. Appl. Stat. 7 (1) 81 - 101, March 2013. https://doi.org/10.1214/12-AOAS588

Information

Published: March 2013
First available in Project Euclid: 9 April 2013

zbMATH: 06171264
MathSciNet: MR3086411
Digital Object Identifier: 10.1214/12-AOAS588

Keywords: EM algorithm , geomarketing , Geostatistics , Hessian estimation , spatial interaction , spatial potential

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.7 • No. 1 • March 2013
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