phat: Estimate Type-Specific Probabilities

In spatialkernel: Nonparametric Estimation of Spatial Segregation in a Multivariate Point Process

Description

Estimate the type-specific probabilities for a multivariate Poisson point process with independent component processes of each type.

Usage

phat(gpts, pts, marks, h)

Arguments

gpts	matrix containing the x,y-coordinates of the point locations at which type-specific probabilities are estimated.
pts	matrix containing the x,y-coordinates of the data points.
marks	numeric/character vector of the types of the point in the data.
h	numeric value of the bandwidth used in the kernel regression.

Details

The type-specific probabilities for data (x_i, m_i), where x_i are the spatial point locations and m_i are the categorical mark sequence numbers, m_i=1,2,…, are estimated using the kernel smoothing methodology \hat p_k(x)=∑_{i=1}^nw_{ik}(x)I(m_i=k), where w_{ik}(x)=w_k(x-x_i)/∑_{j=1}^n w_k(x-x_j), w_k(.) is the kernel function with bandwidth h_k>0, w_k(x)=w_0(x/h_k)/h_k^2, and w_0(\cdot) is the standardised form of the kernel function.

The default kernel is the Gaussian. Different kernels can be selected by calling setkernel.

Value

A list with components

p	matrix of the type-specific probabilities for all types, with the type marks as the matrix row names.
...	copy of the arguments pts, dpts, marks, h.

References

1. Diggle, P. J. and Zheng, P. and Durr, P. A. (2005) Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK. J. R. Stat. Soc. C, 54, 3, 645–658.

See Also

cvloglk, mcseg.test, and setkernel.

spatialkernel documentation built on May 2, 2019, 4:37 p.m.