Hbcv, Hbcv.diag              package:ks              R Documentation

_B_i_a_s_e_d _c_r_o_s_s-_v_a_l_i_d_a_t_i_o_n (_B_C_V) _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:

     BCV bandwidth matrix for bivariate data.

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

     Hbcv(x, whichbcv=1, Hstart)
     Hbcv.diag(x, whichbcv=1, Hstart)

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

       x: matrix of data values

whichbcv: 1 = BCV1, 2 = BCV2.  See details below

  Hstart: initial bandwidth matrix, used in numerical optimisation

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

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

     There are two types of BCV criteria considered here.  They are
     known as BCV1 and BCV2, from Sain, Baggerly & Scott (1994) and
     they only differ slightly. These BCV surfaces can have multiple
     minima and so it can be quite difficult to locate the most
     appropriate minimum.

     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:

     BCV bandwidth matrix.

_N_o_t_e:

     It can be difficult to find an appropriate (local) minimum of the
     BCV criterion. Some times, there can be no local minimum at all so
     there may be no finite BCV selector.

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

     Sain, S.R, Baggerly, K.A. & Scott, D.W. (1994) _Cross-validation
     of multivariate densities_. Journal of the American Statistical
     Association. *82*, 1131-1146.

     Duong, T. & Hazelton, M.L. (2004) _Cross-validation bandwidth
     matrices for multivariate kernel density estimation_. Scandinavian
     Journal  of Statistics. In press.

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

     'Hlscv', 'Hscv'

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

     data(unicef)
     Hbcv(unicef)
     Hbcv.diag(unicef)

