kappa0                package:locfit                R Documentation

_C_r_i_t_i_c_a_l _V_a_l_u_e_s _f_o_r _S_i_m_u_l_t_a_n_e_o_u_s _C_o_n_f_i_d_e_n_c_e _B_a_n_d_s.

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

     The geometric constants for simultaneous confidence bands are
     computed, as described in Sun and Loader (1994) (bias adjustment
     is not implemented here). These are then passed to the `crit'
     function, which computes the critical value for the confidence
     bands.

     The method requires both the weight diagrams l(x), the derivative
     l'(x) and second derivatives l''(x). These are implemented exactly
     for a constant bandwidth; that is, `alpha=c(0,h)' for some `h'.
     For nearest neighbor bandwidths, the computations are approximate.

     The theoretical justification for the bands are computed using the
     spherical symmetry of the Normal distributions. For non-normal
     distributions, and likelihood models, one relies on central limit
     and related theorems...

     Computation uses the product Simpson's rule to evaluate the
     multidimensional integrals. Expect this to be slow in more than
     one dimension. The `mint' argument controls the precision.

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

     kappa0(formula, cov=0.95, ...)

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

 formula: Local regression model formula. 

     cov: Coverage Probability for critical values. 

   ldots: Other arguments to `locfit'. 

_V_a_l_u_e:

     A list with components for the critical value, geometric
     constants, e.t.c. Can be passed directly to `plot.locfit' as the
     `crit' argument.

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

     Sun, J. and Loader, C. (1994). Simultaneous confidence bands for
     linear regression and smoothing. Annals of Statistics 22,
     1328-1345.

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

     `locfit', `plot.locfit', `crit', `crit<-'.

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

     # compute and plot simultaneous confidence bands
     data(ethanol)
     fit <- locfit(NOx~E,data=ethanol)
     crit(fit) <- kappa0(NOx~E,data=ethanol)
     plot(fit,crit=crit,band="local")

