adlift (version 0.8-2)

QuadPred: QuadPred

Description

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

Usage

QuadPred(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 QuadPred, since this is known already from nbrs.

Value

• Xneigh
  matrix of X values corresponding to the neighbours of the removed point. The matrix consists of columns $X[nbrs],X[nbrs]^2$, 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.

Details

The procedure performs quadratic 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 quadratic regression curve, the order of prediction is decreased down to LinearPred.

See Also

CubicPred, fwtnp, LinearPred

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 quadratic prediction based on the neighbours (without intercept) 
#
qp<-QuadPred(order(tx),tx,ty,out$nbrs,173,FALSE,2)
#
#
qp[3:5]
#
#the regression curve details