bkde2D              package:KernSmooth              R Documentation

_C_o_m_p_u_t_e _a _2_D _B_i_n_n_e_d _K_e_r_n_e_l _D_e_n_s_i_t_y _E_s_t_i_m_a_t_e

_D_e_s_c_r_i_p_t_i_o_n:

     Returns the set of grid points in each coordinate direction, and
     the matrix of density estimates over the mesh induced by the grid
     points. The kernel is the standard bivariate normal density.

_U_s_a_g_e:

     bkde2D(x, bandwidth, gridsize=c(51, 51), range.x, truncate=TRUE)

_A_r_g_u_m_e_n_t_s:

       x: a two-column matrix containing the observations from the  
          distribution whose density is to be estimated. Missing values
          are not allowed. 

bandwidth: vector containing the bandwidth to be used in each
          coordinate direction. 

gridsize: vector containing the number of equally spaced points in each
          direction over which the density is to be estimated. 

 range.x: a list containing two vectors, where each vector  contains
          the minimum and maximum values of 'x' at which to compute the
          estimate for each direction. The default minimum in each
          direction is minimum data value minus 1.5 times the bandwidth
          for that direction. The default maximum is the maximum data
          value plus 1.5 times the bandwidth for that direction 

truncate: logical flag: if TRUE, data with 'x' values outside the range
          specified by 'range.x' are ignored. 

_V_a_l_u_e:

     a list containing the following components:

      x1: vector of values of the grid points in the first coordinate
          direction at which the estimate was computed.  

      x2: vector of values of the grid points in the second coordinate
          direction at which the estimate was computed.  

    fhat: matrix of density estimates  over the mesh induced by 'x1'
          and 'x2'. 

_D_e_t_a_i_l_s:

     This is the binned approximation to the 2D kernel density
     estimate. Linear binning is used to obtain the bin counts and the
     Fast Fourier Transform is used to perform the discrete
     convolutions. For each 'x1','x2' pair the bivariate Gaussian
     kernel is centered on that location and the heights of the 
     kernel, scaled by the bandwidths, at each datapoint are summed.
     This sum, after a normalization, is the corresponding  'fhat'
     value in the output.

_R_e_f_e_r_e_n_c_e_s:

     Wand, M. P. (1994). Fast Computation of Multivariate Kernel
     Estimators. _Journal of Computational and Graphical Statistics,_
     *3*, 433-445.

     Wand, M. P. and Jones, M. C. (1995). _Kernel Smoothing._ Chapman
     and Hall, London.

_S_e_e _A_l_s_o:

     'bkde', 'density', 'hist'.

_E_x_a_m_p_l_e_s:

     data(geyser, package="MASS")
     x <- cbind(geyser$duration, geyser$waiting)
     est <- bkde2D(x, bandwidth=c(0.7,7))
     contour(est$x1, est$x2, est$fhat)
     persp(est$fhat)

