hcv                    package: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, hstart = NA, hend = NA, ...) 

_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 nonparametric regression. 

       y: a vector of response values for nonparametric regression. 

  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. 

     ...: other optional parameters are passed to the `sm.options'
          function, through a mechanism which limits their effect only
          to this call of the function;  those relevant for this
          function are the following: 

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 parameter. Default:
          `ngrid=8'. 

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

     add: controls whether the plot is added to an existing graph.
          Default: `add=F'. 

_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 estimate of the value of h which
     minimises the cross-validatory 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))

