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 _a_n_d _t
_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) and AMISE (Asymptotic Mean Integrated
     Squared Error) of kernel density estimates for normal and t
     mixture densities.

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

     ise.mixt(x, H, mus, Sigmas, props, lower, upper, gridsize=c(250,250),
              stepsize)
     iset.mixt(x, H, mus, Sigmas, dfs, props, lower, upper, gridsize=c(250,250),
               stepsize)  
     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

     dfs: vector of degrees of freedom

   props: vector of mixing proportions

    samp: sample size

lower, upper: vectors of lower, upper bounds for numerical integration

gridsize: vector of number of points in each dimension

stepsize: vector of step sizes in each dimension

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

     For normal mixture densities, the ISE, MISE and AMISE all have
     exact formulas.  See Wand & Jones (1995).  For the t mixture
     densities, we resort to using numerical integration, using a
     simple Riemann sum.  A grid is set up and the function values are
     computed and then multiplied by the area of the grid element to
     give an approximation of the volume under the curve.  The
     resolution of the grid is given either by 'gridsize' or
     'stepsize'.

_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 <- 100
     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)
     x <- rmvnorm.mixt(samp, mus, Sigmas, props)
     H <- Hpi(x)
     ise.mixt(x, H, mus, Sigmas, props, stepsize=0.01)
     mise.mixt(H, mus, Sigmas, props, samp)
     amise.mixt(H, mus, Sigmas, props, samp)

     dfs <- c(7,5)
     x <- rmvt.mixt(samp, mus, Sigmas, dfs, props)
     H <- Hpi(x)
     iset.mixt(x, H, mus, Sigmas, dfs, props, lower=c(-5,-5), upper=c(5,5))

