Package:
Version:
1.3-2

### 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.

### 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`.

### Values

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.

`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)
#