lgcpestK            package:InhomCluster            R Documentation

_M_i_n_i_m_u_m _c_o_n_t_r_a_s_t _e_s_t_i_m_a_t_i_o_n _f_o_r _l_o_g _G_a_u_s_s_i_a_n _C_o_x _p_r_o_c_e_s_s.

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

     Minimum contrast estimation based on K-function for log Gaussian
     Cox process with exponential covariance function.

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

     lgcpestK=function(t,K,startpar)

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

       t: vector of distances for which nonparametric estimate of K is
          evaluated

       K: vector of corresponding values of nonparametric estimate of K

startpar: starting  values (sigma^2,alfa) for parameter estimation
          where sigma^2 is variance of Gaussian field and alfa is
          correlation scale parameter.

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

     This function computes minimum contrast estimates of clustering
     parameters for a log Gaussian Cox process with covariance function
     sigma^2 exp(-d/alpha). The contrast is the integrated squared
     distance between the fourth root of a nonparametric estimate of K
     and the fourth root of the theoretical expression for K.

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

     A list with two components 'minimum' and 'Ktheoret'. The first
     components is as provided by the output of 'optim' and the
     estimate is given by 'minimum$par'. The second component is the
     fitted theoretical K function evaluated at 't'.

_A_u_t_h_o_r(_s):

     Rasmus Waagepetersen rw@math.aau.dk <URL:
     http://www.math.aau.dk/~rw>

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

     Waagepetersen, R. (2006) An estimation function approach to
     inference for inhomogeneous Neyman-Scott processes, submitted.

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

     'optim'

