LinearPredmp {adlift}

LinearPredmp

Description

This function performs the prediction lifting step using a linear regression curve given a configuration of neighbours, for multiple point data.

Usage

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

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.

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 LinearPredmp, 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. Note that this is taken to standardise the input when LocalPredmp is called.

g

the group structure of the multiple point data. Note that this is taken to standardise the input when LocalPredmp is called.

Details

The procedure performs linear 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.

Value

Xneigh

matrix of X values corresponding to the neighbours of the removed point. The matrix consists of the column X[newnbrs] 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.

Note

The Matrix is needed for this function.

Author(s)

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

See Also

CubicPredmp, fwtnpmp, QuadPredmp

Examples

#read in data with multiple values...

data(motorcycledata)
times<-motorcycledata$time
accel<-motorcycledata$accel
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

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