LinearPred              package:adlift              R Documentation

_L_i_n_e_a_r_P_r_e_d

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

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

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

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

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

     The procedure performs linear 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.

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

  Xneigh: matrix of X values corresponding to the neighbours of the
          removed point. The matrix consists of the column X[nbrs]
          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', '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 linear regression based on the neighbours (without intercept) 
     #
     lp<-LinearPred(order(tx),tx,ty,out$nbrs,173,FALSE,2)
     #
     #
     lp
     #
     #the regression curve details

