AdaptPredmp              package:adlift              R Documentation

_A_d_a_p_t_P_r_e_d_m_p

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

     This function performs the prediction lifting step over intercept
     and regression order, for multiple point data.

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

     AdaptPredmp(pointsin, X, coefflist, coeff, nbrs, newnbrs, remove, intercept,
      neighbours, mpdet, g)

_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.

coefflist: the list of detail and multiple scaling coefficients at that
          step of the transform.

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

 newnbrs: as nbrs, but repeated according to the multiple point
          structure of the grid.

  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
          'AdaptPredmp', since this is known already from 'nbrs'.

   mpdet: how the mutiple point detail coefficients are computed. 
          Possible values are "ave", in which the multiple detail
          coefficients produced when performing the multiple
          predictions are averaged, or "min", where the overall minimum
          detail coefficient is taken.  

       g: the group structure of the multiple point data.  

_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[newnbrs],X[newnbrs]^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 'AdaptPredmp'
          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:

     'AdaptNeighmp', 'CubicPredmp', 'fwtnpmp', 'LinearPredmp',
     'QuadPredmp'

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

     #read in data with multiple values...

     mcdata()

     short<-adjustx(times,accel,"mean")
     X<-short$sepx
     coeff<-short$sepx
     g<-short$g

     coefflist<-list()
     for (i in 1:length(g)){
     coefflist[[i]]<-accel[g[[i]]]
     }

     #work out neighbours of point to be removed (31)

     out<-getnbrs(X,31,order(X),2,TRUE)
     nbrs<-out$n

     nbrs

     newnbrs<-NULL
     for (i in 1:length(nbrs)){
     newnbrs<-c(newnbrs,rep(nbrs[i],times=length(g[[nbrs[i]]])))
     }

     #work out repeated neighbours using g...
     newnbrs

     AdaptPredmp(order(X),X,coefflist,coeff,nbrs,newnbrs,31,TRUE,2,"ave",g)

