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