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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Métodos Cuantitativos para la Economía y la EmpresaPatrocinadores
The authors would like to express their thanks to the project ECO2009-10534 of the Ministerio de Ciencia e Innovación del Reino de España.Fecha de publicación
2012-03Editorial
INECita bibliográfica
LÓPEZ, 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 2254-9390Revisión por pares
siPalabras clave
Categorical dataSpatial independence
Distribution-free
Business establishments
Firm micro-data
Madrid
Resumen
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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