CubicPred {adlift} | R Documentation |
This function performs the prediction lifting step using a cubic regression curve given a configuration of neighbours.
CubicPred(pointsin, X, coeff, nbrs, remove, intercept, neighbours)
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 . |
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
).
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. |
Matt Nunes (matt.nunes@bristol.ac.uk), Marina Popa (Marina.Popa@bristol.ac.uk)
# # 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 #