# phat

0th

Percentile

##### Estimate Type-Specific Probabilities

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

Keywords
multivariate, regression, smooth, spatial, nonparametric
##### 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, $m_i=1,2,\ldots$, are estimated using the kernel smoothing methodology $\hat p_k(x)=\sum_{i=1}^nw_{ik}(x)I(m_i=k)$, where $w_{ik}(x)=w_k(x-x_i)/\sum_{j=1}^n w_k(x-x_j)$, $w_k(.)$ 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