Hpi, Hpi.diag               package:ks               R Documentation

_P_l_u_g-_i_n _b_a_n_d_w_i_d_t_h _m_a_t_r_i_x _s_e_l_e_c_t_o_r _f_o_r _b_i_v_a_r_i_a_t_e _d_a_t_a

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

     Plug-in bandwidth matrix for bivariate data.

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

     Hpi(x, nstage=2, pilot="samse", pre="sphere", Hstart)
     Hpi.diag(x, nstage=2, pilot="amse", pre="scale", Hstart)

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

       x: matrix of data values

  nstage: number of stages in the plug-in bandwidth selector (1 or 2)

   pilot: '"amse"' = AMSE-optimal pilot bandwidths, '"samse"' = single
          SAMSE-optimal pilot bandwidth

     pre: '"scale"' = pre-scaling, '"sphere"' = pre-sphering

  Hstart: initial bandwidth matrix, used in numerical optimisation

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

     Use 'Hpi' for full bandwidth matrices and 'Hpi.diag' for diagonal
     bandwidth matrices.

     For AMSE pilot bandwidths, see Wand & Jones (1994). For SAMSE
     pilot bandwidths, see Duong & Hazelton (2003).  The latter is a
     modification of the former, in order to remove any possible
     problems with non-positive definiteness. Both of these pilot
     bandwidths require numerical optimisation. 

     For details on the pre-transformations in 'pre', see 'pre.sphere'
     and 'pre.scale'.

     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:

     Plug-in bandwidth matrix.

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

     Wand, M.P. & Jones, M.C. (1994) _Multivariate plugin bandwidth
     selection_.  Computational Statistics *9*, 97-116.

     Duong, T. & Hazelton, M.L. (2003) _Plug-in bandwidth matrices for
     bivariate kernel density estimation_. Journal of Nonparametric
     Statistics *15*, 17-30.

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

     data(unicef)
     Hpi(unicef, nstage=1, pilot="amse", pre="scale")
     Hpi(unicef, nstage=2, pilot="samse", pre="sphere")
     Hpi.diag(unicef, nstage=2, pilot="amse", pre="scale") 

