# Evaluate the fit for iterative bias reduction model

### Description

The function evaluates the fit for iterative bias reduction
model for iteration `k`

. This function is not intended to be used directly.

### Usage

1 | ```
fittedS1lr(n,U,tUy,eigenvaluesS1,ddlmini,k,rank)
``` |

### Arguments

`n` |
The number of observations. |

`U` |
The the matrix of eigen vectors of the
symmetric smoothing matrix |

`tUy` |
The transpose of the matrix of eigen vectors of the
symmetric smoothing matrix |

`eigenvaluesS1` |
Vector of the eigenvalues of the
symmetric smoothing matrix |

`ddlmini` |
The number of eigen values of |

`k` |
A numeric vector which gives the number of iterations |

`rank` |
The rank of lowrank splines. |

### Details

see the reference for detailed explanation of computation of iterative bias reduction smoother

### Value

Returns a vector containing the fit

### 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.

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

### See Also

`ibr`