Statistica Sinica 27 (2017), 555-574
Abstract: We introduce a single index model for the intensity of an inhomogeneous spatial point process, relating the intensity function to an unknown function of a linear combination of measurements of a -dimensional spatial covariate process. Such a model extends and generalizes a commonly used model where is known. We derive an estimating procedure for and the coefficient parameters and show consistency and asymptotic normality of estimates of under some regularity assumptions. We present results of some simulation studies showing the effectiveness of the procedure. Finally, we apply the procedure to a dataset of fast food restaurant locations in New York City.
Key words and phrases: Asymptotic normality, consistency, fast food restaurant data, single-index model, spatial point processes.