# 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