Hmise.mixt, Hamise.mixt          package:ks          R Documentation

_M_I_S_E- _a_n_d _A_M_I_S_E-_o_p_t_i_m_a_l _b_a_n_d_w_i_d_t_h _m_a_t_r_i_x _s_e_l_e_c_t_o_r_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:

     For normal mixture densities, we have a closed form for the MISE
     and AMISE. So in these cases, we can numerically minimise these
     criteria to find MISE- and AMISE-optimal matrices.

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

     Hmise.mixt(mus, Sigmas, props, samp, Hstart)
     Hamise.mixt(mus, Sigmas, props, samp, Hstart)

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

     mus: (stacked) matrix of mean vectors

  Sigmas: (stacked) matrix of variance matrices

   props: vector of mixing proportions

    samp: sample size

  Hstart: initial bandwidth matrix, used in numerical optimisation

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

     For normal mixture densities, the MISE and AMISE have exact
     formulas. See Wand & Jones (1995).

     If 'Hstart' is not given then it defaults to 'k*var(x)' where k =
     4/(n*(d + 2))^(2/(d+ 4)), n = sample size, d = dimension of data.

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

     Full MISE- or AMISE-optimal bandwidth matrix. Please note that
     diagonal forms of these matrices are not available.

_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:

     mus <- rbind(c(-3/2,0), c(3/2,0))
     Sigmas <- rbind(diag(c(1/16, 1)), rbind(c(1/16, 1/18), c(1/18, 1/16)))
     props <- c(2/3, 1/3)
     samp <- 100
     Hmise.mixt(mus, Sigmas, props, samp)
     Hamise.mixt(mus, Sigmas, props, samp)

