

hcv(sm)                                      R Documentation

_C_r_o_s_s_-_v_a_l_i_d_a_t_o_r_y _c_h_o_i_c_e _o_f _s_m_o_o_t_h_i_n_g _p_a_r_a_m_e_t_e_r

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

     This function uses the technique of cross-validation to
     select a smoothing parameter suitable for constructing
     a density estimate or nonparametric regression curve in
     one or two dimensions.

_U_s_a_g_e_:

     hcv(x, y=NA, h.weights=NA, ngrid=8, hstart=NA, hend=NA, display="none", add=F, ...)

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

       x: a vector, or two-column matrix of data.  If `y' is
          missing these are observations to be used in the
          construction of a density estimate.  If `y' is
          present, these are the covariate values for a non-
          parametric regression.

       y: a vector of response values for nonparametric
          regression.

h.weights: a vector of weights which multiply the smoothing
          parameter(s) used in the kernel function at each
          observation.

   ngrid: the number of grid points to be used in an initial
          grid search for the value of the smoothing parame-
          ter.

  hstart: the smallest value of the grid points to be used
          in an initial grid search for the value of the
          smoothing parameter.

    hend: the largest value of the grid points to be used in
          an initial grid search for the value of the
          smoothing parameter.

 display: any character setting other than `"none"' will
          cause the criterion function to be plotted over
          the search grid of smoothing parameters.  The par-
          ticular value `"log"' will use a log scale for the
          grid values.

     add: controls whether the plot is added to an existing
          graph.

     ...: additional graphical parameters.

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

     see Sections 2.4 and 4.5 of the reference below.

     The two-dimensional case uses a smoothing parameter
     derived from a single value, scaled by the standard
     deviation of each component.

     This function does not employ a sophisticated algorithm
     and some adjustment of the search parameters may be
     required for different sets of data.  An initial esti-
     mate of the value of h which minimises the cross-val-
     idatory criterion is located from a grid search using
     values which are equally spaced on a log scale between
     `hstart' and `hend'.  A quadratic approximation is then
     used to refine this initial estimate.

_V_a_l_u_e_:

     the value of the smoothing parameter which minimises
     the cross-validation criterion over the selected grid.

_S_i_d_e _E_f_f_e_c_t_s_:

     If the minimising value is located at the end of the
     grid of search positions, or if some values of the
     cross-validatory criterion cannot be evaluated, then a
     warning message is printed.  In these circumstances
     altering the values of `hstart' and `hend' may improve
     performance.

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

     Bowman, A.W. and Azzalini, A. (1997). Applied Smoothing
     Techniques for Data Analysis: the Kernel Approach with
     S-Plus Illustrations.  Oxford University Press, Oxford.

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

     `cv', `hsj', `hnorm'

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

     #  Density estimation

     x <- rnorm(50)
     par(mfrow=c(1,2))
     h.cv <- hcv(x, display="lines", ngrid=32)
     sm.density(x, h=hcv(x))
     par(mfrow=c(1,1))

     #  Nonparametric regression

     x <- seq(0, 1, length = 50)
     y <- rnorm(50, sin(2 * pi * x), 0.2)
     par(mfrow=c(1,2))
     h.cv <- hcv(x, y, display="lines", ngrid=32)
     sm.regression(x, y, h=hcv(x, y))
     par(mfrow=c(1,1))

