TY - JOUR
T1 - A thinned block bootstrap variance estimation procedure for inhomogeneous spatial point patterns
AU - Guan, Yongtao
AU - Loh, Ji Meng
N1 - Funding Information:
Yongtao Guan is Assistant Professor, Division of Biostatistics, Yale University, New Haven, CT 06520 (E-mail: [email protected]). Ji Meng Loh is Associate Professor, Department of Statistics, Columbia University, New York, NY 10027. Guan’s research was supported in part by National Science Foundation (NSF) grant DMS-0706806; Ji Meng Loh’s research was supported in part by NSF grant AST-0507687. The authors thank Steve Rathbun, Mike Sherman, and Rasmus Waagepetersen for helpful discussions and the joint editors, associate editor, and three referees for their constructive comments that have greatly improved the manuscript.
PY - 2007/12
Y1 - 2007/12
N2 - When modeling inhomogeneous spatial point patterns, it is of interest to fit a parametric model for the first-order intensity function (FOIF) of the process in terms of some measured covariates. Estimates for the regression coefficients, say β, can be obtained by maximizing a Poisson maximum likelihood criterion. Little work has been done on the asymptotic distribution of β except in some special cases. In this article we show that β is asymptotically normal for a general class of mixing processes. To estimate the variance of β, we propose a novel thinned block bootstrap procedure that assumes that the point process is second-order reweighted stationary. To apply this procedure, only the FOIF, and not any high-order terms of the process, needs to be estimated. We establish the consistency of the resulting variance estimator, and demonstrate its efficacy through simulations and an application to a real data example.
AB - When modeling inhomogeneous spatial point patterns, it is of interest to fit a parametric model for the first-order intensity function (FOIF) of the process in terms of some measured covariates. Estimates for the regression coefficients, say β, can be obtained by maximizing a Poisson maximum likelihood criterion. Little work has been done on the asymptotic distribution of β except in some special cases. In this article we show that β is asymptotically normal for a general class of mixing processes. To estimate the variance of β, we propose a novel thinned block bootstrap procedure that assumes that the point process is second-order reweighted stationary. To apply this procedure, only the FOIF, and not any high-order terms of the process, needs to be estimated. We establish the consistency of the resulting variance estimator, and demonstrate its efficacy through simulations and an application to a real data example.
KW - Block bootstrap
KW - Inhomogeneous spatial point process
KW - Thinning
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U2 - 10.1198/016214507000000879
DO - 10.1198/016214507000000879
M3 - Article
AN - SCOPUS:38349060775
SN - 0162-1459
VL - 102
SP - 1377
EP - 1386
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 480
ER -