iterchoiceS1lrcve {ibr}

Selection of the number of iterations for iterative bias reduction smoothers with base lowrank thin-plate splines smoother or duchon splines smoother

Description

Evaluates at each iteration proposed in the grid the cross-validated root mean squared error (RMSE) and mean of the relative absolute error (MAP). The minimum of these criteria gives an estimate of the optimal number of iterations. This function is not intended to be used directly.

Usage

iterchoiceS1lrcve(X, y, lambda, rank, bs, listvarx, df, ddlmini, ntest, ntrain,
Kfold, type, npermut, seed, Kmin, Kmax, m, s)

Arguments

X

A numeric matrix of explanatory variables, with n rows and p columns.

y

A numeric vector of variable to be explained of length n.

lambda

A numeric positive coefficient that governs the amount of penalty (coefficient lambda).

rank

The rank of lowrank splines.

bs

The type rank of lowrank splines: tps or ds.

listvarx

The vector of the names of explanatory variables

df

A numeric vector of length 1 which is multiplied by the minimum df of thin plate splines ; This argument is useless if lambda is supplied (non null).

ddlmini

The number of eigenvalues equals to 1.

ntest

The number of observations in test set.

ntrain

The number of observations in training set.

Kfold

Either the number of folds or a boolean or NULL.

type

A character string in random,timeseries,consecutive, interleaved and give the type of segments.

npermut

The number of random draw (with replacement), used for type="random".

seed

Controls the seed of random generator (via set.seed).

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.

m

The order of derivatives for the penalty (for thin plate splines it is the order). This integer m must verify 2m+2s/d>1, where d is the number of explanatory variables.

s

The power of weighting function. For thin plate splines s is equal to 0. This real must be strictly smaller than d/2 (where d is the number of explanatory variables) and must verify 2m+2s/d. To get pseudo-cubic splines, choose m=2 and s=(d-1)/2 (See Duchon).

Value

Returns the values of RMSE and MAP for each value of the grid K. Inf are returned if the iteration leads to a smoother with a df bigger than ddlmaxi.

Author(s)

Pierre-Andre Cornillon, Nicolas Hengartner and Eric Matzner-Lober.

References

Cornillon, P.-A.; Hengartner, N.; Jegou, N. and Matzner-Lober, E. (2012) Iterative bias reduction: a comparative study. Statistics and Computing, 23, 777-791.

Cornillon, P.-A.; Hengartner, N. and Matzner-Lober, E. (2013) Recursive bias estimation for multivariate regression smoothers Recursive bias estimation for multivariate regression smoothers. ESAIM: Probability and Statistics, 18, 483-502.

Cornillon, P.-A.; Hengartner, N. and Matzner-Lober, E. (2017) Iterative Bias Reduction Multivariate Smoothing in R: The ibr Package. Journal of Statistical Software, 77, 1–26.

Duchon, J. (1977) Splines minimizing rotation-invariant semi-norms in Solobev spaces. in W. Shemp and K. Zeller (eds) Construction theory of functions of several variables, 85-100, Springer, Berlin.

Wood, S.N. (2003) Thin plate regression splines. J. R. Statist. Soc. B, 65, 95-114.

See Also

ibr