No. 1106

Title:

Identification and estimation of superposed Neyman-Scott spatial cluster processes

Author(s):

Tanaka, Ushio (The Institute of Statistical Mathematics);
Ogata, Yosihiko (The Institute of Statistical Mathematics)

Key words:

contact distances; likelihood functions; multi-type Neyman-Scott processes; nearest neighbour distance function; Palm intensity

Abstract:

    This paper proposes an estimation method of superposed spatial point patterns of Neyman-Scott cluster processes of different distance scales and cluster sizes. Unlike the ordinary single Neyman-Scott model, the superposed process of Neyman-Scott models is not identified solely by the second order moment property of the process. To solve the identification problem we make use of the nearest neighbor distance property in addition to the second order moment property. In the present procedure, we combine a non stationary Poisson likelihood based on the Palm intensity with another likelihood function based on the nearest neighbor property. The derivative of the nearest neighbor distance function is regarded as the intensity function of the rotation invariant non-homogeneous Poisson point process. The present estimation procedure is applied to a couple of ecological location data.