sreg                 package:funfits                 R Documentation

_S_m_o_o_t_h_i_n_g _s_p_l_i_n_e _r_e_g_r_e_s_s_i_o_n

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

     A smoothing spline is a locally weighted average of the data y's
     based on the relative locations of the x values. Formally the
     estimate is the curve that minimizes the criterion: (1/n)
     sum(k=1,n) ( Y_k - f( X_k))**2  + lambda* R(f) where R(f) is the
     integral of the squared second derivative of f over the range of
     the X values. The solution is a piecewise cubic polynomial with
     the join points at the unique set of X values. The polynomial
     segments are constructed so that the entire curve has continuous
     first and second derivatives and the second and third derivatives
     are zero at the boundaries.  The smoothing has the range
     [0,infinity]. Lambda equal to  zero gives a cubic spline
     interpolation of  the data. As lambda diverges to infinity ( e.g
     lambda =1e20) the  estimate will converge to the straight line
     estimated by least squares.

     The values of the estimated function at the data points can be
     expressed in the matrix form:

     predicted.values= A(lambda)Y where A is an nXn symmetric matrix
     that does NOT depend on Y. The diagonal elements are the leverage
     values for the estimate and the sum of these  (trace(A(lambda))
     can be interpreted as the effective number of parameters that are
     used to define the spline function.

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

     sreg(x, y, lam=NA, offset=0, wt=rep(1, length(x)), cost=1, nstep.cv=50, maxit.cv=10, xgrid=sort(unique(x)), deriv=0, find.trA=T)

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

       x: Vector of x values 

       y: Vector of y values 

     lam: Smoothing parameter. If omitted this is estimated by GCV. 

  offset: GCV is RSS/((1-(tr(A)-offset)*cost + offset)/n)^2, so that
          the degrees of freedom can be adjusted with the offset. 

      wt: A vector that is proportional to the standard deviation of
          the errors. 

    cost: Cost value to be used in the GCV criterion. 

nstep.cv: Number of grid points for minimum GCV search 

maxit.cv: Maximum number of iterations for Golden Section search of
          optimum 

   xgrid: Vector of points to evaluate the estimated curve. Default is
          unique sorted x's. 

   deriv: If equal to 1 or 2 returns the estimated first or second
          derivative of the estimate.  

find.trA: Calculate the trace of A 

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

     Returns a list of class sreg. This includes the predicted values
     and  residuals. The lambda and the effective number of parameters
     for the fit are also returned. The results of the grid search to
     minimize GCV are returned in cv.grid.

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

     Additive Models by Hastie and Tibishirani

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

     splint, tps

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

     sreg(ozone$x[,1],ozone$y)-> fit # fit sreg to ozone at longitude values
     plot(fit)                       # plot sreg fit

