

spreg(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 val-
     ues. 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 polyno-
     mial segments are constructed so that the entire curve
     has continuous first and second derivatives and the
     second and third derivatives are zero at the bound-
     aries.  The smoothing parameter has the range [0,infin-
     ity]. Lambda equal to  zero gives a cubic spline inter-
     polation 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 symmet-
     ric 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_:

     spreg(x, y, lambda, xgrid, weight=rep(1, length(x)), derivative=0,
     Adiag=T, cost=1)

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

       x: Vector of x values

       y: Vector of y values

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

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

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

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

   Adiag: If true will compute leverage values for the esti-
          mate

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

_V_a_l_u_e_:

     A list of class spreg. The values of the GCV function
     and the effective number of parameters are tabulated in
     the component gcv.grid.  The component predicted is a
     two column matrix that contains the values from xgrid
     (or sorted unique x's) and the estimated curve at these
     points.

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

     Additive Models by Hastie and Tibishirani

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

     predict.spreg, splint, tpsreg

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

     spreg( auto.paint$thick, auto.paint$DOI)-> out
     plot(out)
     lines(out$predicted)

