Description Usage Arguments Value Author(s) References See Also Examples
Performs iterative bias reduction using kernel, thin plate splines Duchon splines or low rank splines. Missing values are not allowed.
1 2 
formula 
An object of class 
data 
An optional data frame, list or environment (or object
coercible by 
subset 
An optional vector specifying a subset of observations to be used in the fitting process. 
criterion 
A vector of string. If the number of iterations
( 
df 
A numeric vector of either length 1 or length equal to the
number of columns of 
Kmin 
The minimum number of bias correction iterations of the search grid considered by the model selection procedure for selecting the optimal number of iterations. 
Kmax 
The maximum number of bias correction iterations of the search grid considered by the model selection procedure for selecting the optimal number of iterations. 
smoother 
Character string which allows to choose between thin plate
splines 
kernel 
Character string which allows to choose between gaussian kernel
( 
rank 
Numeric value that control the rank of low rank splines
(denoted as 
control.par 
A named list that control optional parameters. The
components are

cv.options 
A named list which controls the way to do cross
validation with component 
Returns an object of class ibr
which is a list including:
beta 
Vector of coefficients. 
residuals 
Vector of residuals. 
fitted 
Vector of fitted values. 
iter 
The number of iterations used. 
initialdf 
The initial effective degree of freedom of the pilot (or base) smoother. 
finaldf 
The effective degree of freedom of the iterated bias reduction
smoother at the 
bandwidth 
Vector of bandwith for each explanatory variable 
call 
The matched call 
parcall 
A list containing several components:

criteria 
Value
of the chosen criterion at the given iteration, 
alliter 
Numeric vector giving all the optimal number of iterations selected by the chosen criteria. 
allcriteria 
either a list containing all the criteria evaluated on the
grid 
call 
The matched call. 
terms 
The 'terms' object used. 
PierreAndre Cornillon, Nicolas Hengartner and Eric MatznerLober.
Cornillon, P.A.; Hengartner, N.; Jegou, N. and MatznerLober, E. (2012) Iterative bias reduction: a comparative study. Statistics and Computing, 23, 777791.
Cornillon, P.A.; Hengartner, N. and MatznerLober, E. (2013) Recursive bias estimation for multivariate regression smoothers Recursive bias estimation for multivariate regression smoothers. ESAIM: Probability and Statistics, 18, 483502.
Cornillon, P.A.; Hengartner, N. and MatznerLober, E. (2017) Iterative Bias Reduction Multivariate Smoothing in R: The ibr Package. Journal of Statistical Software, 77, 1–26.
Wood, S.N. (2003) Thin plate regression splines. J. R. Statist. Soc. B, 65, 95114.
predict.ibr
, summary.ibr
, gam
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28  f < function(x, y) { .75*exp(((9*x2)^2 + (9*y2)^2)/4) +
.75*exp(((9*x+1)^2/49 + (9*y+1)^2/10)) +
.50*exp(((9*x7)^2 + (9*y3)^2)/4) 
.20*exp(((9*x4)^2 + (9*y7)^2)) }
# define a (fine) xy grid and calculate the function values on the grid
ngrid < 50; xf < seq(0,1, length=ngrid+2)[c(1,ngrid+2)]
yf < xf ; zf < outer(xf, yf, f)
grid < cbind.data.frame(x=rep(xf, ngrid),y=rep(xf, rep(ngrid, ngrid)),z=as.vector(zf))
persp(xf, yf, zf, theta=130, phi=20, expand=0.45,main="True Function")
#generate a data set with function f and noise to signal ratio 5
noise < .2 ; N < 100
xr < seq(0.05,0.95,by=0.1) ; yr < xr ; zr < outer(xr,yr,f) ; set.seed(25)
std < sqrt(noise*var(as.vector(zr))) ; noise < rnorm(length(zr),0,std)
Z < zr + matrix(noise,sqrt(N),sqrt(N))
# transpose the data to a column format
xc < rep(xr, sqrt(N)) ; yc < rep(yr, rep(sqrt(N),sqrt(N)))
data < cbind.data.frame(x=xc,y=yc,z=as.vector(Z))
# fit by thin plate splines (of order 2) ibr
res.ibr < ibr(z~x+y,data=data,df=1.1,smoother="tps")
fit < matrix(predict(res.ibr,grid),ngrid,ngrid)
persp(xf, yf, fit ,theta=130,phi=20,expand=0.45,main="Fit",zlab="fit")
## Not run:
data(ozone, package = "ibr")
res.ibr < ibr(Ozone~.,data=ozone,df=1.1)
summary(res.ibr)
predict(res.ibr)
## End(Not run)

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