Description Usage Arguments Details Value References See Also

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

1 | ```
phat(gpts, pts, marks, h)
``` |

`gpts` |
matrix containing the |

`pts` |
matrix containing the |

`marks` |
numeric/character vector of the types of the point in the data. |

`h` |
numeric value of the bandwidth used in the kernel regression. |

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`

.

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`

.

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`

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