# phat: Estimate Type-Specific Probabilities In spatialkernel: Non-Parametric 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

 1 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.

cvloglk, mcseg.test, and setkernel