Distribution-free inference for Q(m) based on permutational bootstrappingan application to the spatial co-location pattern of firms in Madrid
- Fernando A. López
- Antonio Páez
ISSN: 0014-1151
Year of publication: 2012
Volume: 54
Issue: 177
Pages: 135-156
Type: Article
More publications in: Estadística española
Abstract
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 categories and smaller sample sizes. The proposed approach is demonstrated empirically using a case study of co-location of business establishments in Madrid.