CubicPred {adlift}

CubicPred

Description

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

Usage

CubicPred(pointsin, X, coeff, nbrs, remove, intercept, 
neighbours)

Arguments

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.

Details

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).

Value

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.

Author(s)

Matt Nunes ([e-mail]), Marina Knight

See Also

fwtnp, LinearPred, QuadPred

Examples

#
# 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
#