ise, mise, amise             package:ks             R Documentation

_I_S_E, _M_I_S_E _a_n_d _A_M_I_S_E _o_f _k_e_r_n_e_l _d_e_n_s_i_t_y _e_s_t_i_m_a_t_e_s _f_o_r _n_o_r_m_a_l _m_i_x_t_u_r_e _d_e_n_s_i_t_i_e_s

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

     The global errors ISE (Integrated Squared Error), MISE (Mean
     Integrated Squared Error) of kernel density estimates for normal
     densities, for 2- to 6-dimensional data, and and AMISE (Asymptotic
     Mean Integrated Squared Error) fpr 2-dimensional data.

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

     ise.mixt(x, H, mus, Sigmas, props)  
     mise.mixt(H, mus, Sigmas, props, samp)
     amise.mixt(H, mus, Sigmas, props, samp)

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

       x: matrix of data values

       H: bandwidth matrix

     mus: (stacked) matrix of mean vectors

  Sigmas: (stacked) matrix of variance matrices

   props: vector of mixing proportions

    samp: sample size

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

     For normal mixture densities, ISE and MISE  have exact formulas
     for all dimensions, and AMISE has an exact form for 2 dimensions.
     See Wand & Jones (1995).

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

     ISE, MISE or AMISE value.

_N_o_t_e:

     Remember that ISE is a random variable that depends on the data
     'x'; and that MISE and AMISE are non-random and don't depend on
     the data.

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

     Wand, M.P. & Jones, M.C. (1995) _Kernel Smoothing_. Chapman &
     Hall. London.

_E_x_a_m_p_l_e_s:

     samp <- 50
     d <- 3
     mus <- rbind(rep(0,d), rep(1,d))
     Sigmas <- 0.25*rbind(diag(d), diag(d))
     props <- c(2/3, 1/3)
     x <- rmvnorm.mixt(samp, mus, Sigmas, props)
     H <- Hpi(x)
     ise.mixt(x, H, mus, Sigmas, props)
     mise.mixt(H, mus, Sigmas, props, samp)

