AdaptPred               package:adlift               R Documentation

_A_d_a_p_t_P_r_e_d

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

     This function performs the prediction lifting step over intercept
     and regression order.

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

     AdaptPred(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. Note that the value to this input is not
          important, since the procedure checks the neighbourhoods
          structure in the minimisation step anyway, but is for
          standardisation of arguments to the non-adaptive prediction
          schemes. 

  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. (Note that this is actually
          a dummy argument, since it is not necessary for the
          computation of the detail coefficient in 'AdaptPred'(the
          intercept is part of the adaptiveness), though is used for
          standardising its arguments with other prediction schemes for
          use in the 'fwtnp' function).

neighbours: the number of neighbours to be considered in the
          computation of predicted values and detail coefficients.

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

     The procedure performs adaptive regression (through AdaptPred)
     over the three types of regression and also over intercept.  The
     combination (type of regression, intercept) is chosen which gives
     the smallest detail coefficient (in absolute value).

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

results.: _This is a ten item list giving the regression information
          chosen from the detail coefficient minimisation:_

  Xneigh: matrix of 'X' values corresponding to the neighbours of the
          removed point. The matrix consists of columns
          1,X[nbrs],X[nbrs]^2,... depending on the order of the
          prediction used and whether or not 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. 

     int: if TRUE, an intercept was used in the regression. 

  scheme: a character vector denoting the type of regression used in
          the prediction ("Linear", "Quad" or "Cubic"). 

 details: a vector of the detail coefficients from which 'AdaptPred'
          selects the minimum value. There are six entries. The first
          three entries represent the detail coefficients from
          regression with no intercept in increasing order of
          prediction. The second three details are values for
          regression with intercept. 

minindex: the index into details ('results[[9]]') which produces the
          minimum value.

_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:

     'AdaptNeigh', 'CubicPred', '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 the adaptive lifting step 
     #
     ap<-AdaptPred(order(tx),tx,ty,out$nbrs,173,FALSE,2)
     #
     ap[[10]]

     #this corresponds to no intercept and highest order regression (Cubic)...
     #
     #and let's check it...
     ap[[7]]

     ap[[8]]

