phat              package:spatialkernel              R Documentation

_E_s_t_i_m_a_t_e _T_y_p_e-_S_p_e_c_i_f_i_c _P_r_o_b_a_b_i_l_i_t_i_e_s

_D_e_s_c_r_i_p_t_i_o_n:

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

_U_s_a_g_e:

     phat(gpts, pts, marks, h)

_A_r_g_u_m_e_n_t_s:

    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.

_D_e_t_a_i_l_s:

     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)=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'.

_V_a_l_u_e:

     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'.

_R_e_f_e_r_e_n_c_e_s:

        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.   

_S_e_e _A_l_s_o:

     'cvloglk', 'mcseg.test', and 'setkernel'.

