Distribution-free inference for Q(m) based on permutational bootstrapping: an application to the spatial co-location pattern of firms in Madrid
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Knowledge AreaMétodos Cuantitativos para la Economía y la Empresa
SponsorsThe authors would like to express their thanks to the project ECO2009-10534 of the Ministerio de Ciencia e Innovación del Reino de España.
Bibliographic CitationLÓPEZ, F.A., PÁEZ, A. Distribution-free inference for Q(m) based on permutational bootstrapping: an application to the spatial co-location pattern of firms in Madrid. En Estadística española. Madrid: INE, 2012, vol. 54, n. 177, pp. 135-156. ISSN 2254-9390
The objective of this paper is to present a distribution-free inferential framework for the Q(m) statistic based on permutational bootstrapping. Q(m) was introduced in the literature as a tool to test for spatial association of qualitative variables, or more precisely, patterns of co-location/co-occurrence. The existing inferential framework for this statistic is based on asymptotic results. A challenge for these results is the need to limit the overlap in the neighborhoods of proximate observations, which tends to reduce the size of the sample, with consequent impacts on the size and power of the statistic. A computationally intensive inferential framework, such as presented in this paper, allows for greater versatility of Q(m). We show that under the bootstrap version the issues with size are ameliorated and the test is more powerful. Furthermore, in this framework there is no longer the need to control for overlap, which allows for applications to variables with more ...
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