QuadPred               package:adlift               R Documentation

_Q_u_a_d_P_r_e_d

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

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

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

     QuadPred(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
          'QuadPred', since this is known already from 'nbrs'.

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

     The procedure performs quadratic 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 quadratic regression curve, the order of prediction is
     decreased down to '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, 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:

     'CubicPred', 'fwtnp', 'LinearPred'

_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 quadratic prediction based on the neighbours (without intercept) 
     #
     qp<-QuadPred(order(tx),tx,ty,out$nbrs,173,FALSE,2)
     #
     #
     qp[3:5]
     #
     #the regression curve details

