CubicPred               package:adlift               R Documentation

_C_u_b_i_c_P_r_e_d

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

     This function performs the prediction lifting step using a cubic
     regression curve given a configuration of neighbours.

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

     CubicPred(pointsin, X, coeff, nbrs, remove, intercept, neighbours)

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

pointsin: The indices of gridpoints still to be removed.

       X: the vector of grid values.

   coeff: the vector of detail and scaling coefficients at that step of
          the transform.

    nbrs: the indices (into 'X') of the neighbours to be used in the
          prediction step.

  remove: the index (into 'X') of the point to be removed.

intercept: Boolean value for whether or not an intercept is used in the
          prediction step of the transform. 

neighbours: the number of neighbours in the computation of the
          predicted value. This is not actually used specifically in
          'CubicPred', since this is known already from 'nbrs'.

_D_e_t_a_i_l_s:

     The procedure performs cubic regression using the given neighbours
     using an intercept if chosen. The regression coefficients
     ('weights') are used to predict the new function value at the
     removed point. If there are not enough neighbours to generate a
     cubic regression curve, the order of prediction is decreased until
     it is possible (i.e. to 'QuadPred', then 'LinearPred').

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

  Xneigh: matrix of 'X' values corresponding to the neighbours of the
          removed point. The matrix consists of columns
          X[nbrs],X[nbrs]^2,X[nbrs]^3 augmented with a column of ones
          if an intercept is used. Refer to any reference on linear
          regression for more details.

      mm: the matrix from which the prediction is made. In terms of
          'Xneigh', it is (Xneigh^T Xneigh)^{-1} Xneigh^T .

    bhat: The regression coefficients used in prediction.

 weights: the prediction weights for the neighbours.

    pred: the predicted function value obtained from the regression.

   coeff: vector of (modified) detail and scaling coefficients to be
          used in the update step of the transform.

_A_u_t_h_o_r(_s):

     Matt Nunes (matt.nunes@bristol.ac.uk), Marina Popa
     (Marina.Popa@bristol.ac.uk)

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

     'fwtnp', 'LinearPred', 'QuadPred'

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

     #
     # Generate some doppler data: 500 observations.
     #
     tx <- runif(500)
     ty<-make.signal2("doppler",x=tx)
     #
     # Compute the neighbours of point 173 (2 neighbours on each side)
     #
     out<-getnbrs(tx,173,order(tx),2,FALSE)

     #
     # Perform cubic prediction based on the neighbours (without intercept) 
     #
     cp<-CubicPred(order(tx),tx,ty,out$nbrs,173,FALSE,2)
     #
     cp$bhat

     #
     #the coefficients which define the cubic regression curve
     #
     cp$pred

     #
     #the predicted value from the regression curve
     #

