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 (in 2 or more dimensions) the 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 and a warning is produced.

     The theoretical justification for the bands uses normality of the
     random errors e_1,...,e_n in the regression model, and in
     particular the spherical symmetry of the error vector. 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 (The domain of integration, and hence
     the region of simultaneous coverage, is determined by the 'flim'
     argument). Expect the integration 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. A '"locfit"' object can also
          be provided; in this case the formula and other arguments are
          extracted from this object. 

     cov: Coverage Probability for critical values.  

     ...: Other arguments to 'locfit'. Important arguments include
          'flim' and 'alpha'. 

_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")

