# Fit Free-Knot Splines To Data

### Description

These functions fit free-knot splines to data with one independent variable and one dependent variable. It is assumed that the number of knots is known in advance. `freelsgen`

and `freelsgold`

fit least-squares splines with no penalty, while `freepsgen`

and `freepsgold`

fit penalized splines. `freelsgen`

and `freepsgen`

use a genetic algorithm, while `freelsgold`

and `freepsgold`

use a blind search augmented with a golden section algorithm.

### Usage

1 2 3 4 | ```
freelsgen(x, y, degree, numknot, seed = 5, stream = 0)
freelsgold(x, y, degree, numknot, seed = 5, stream = 0)
freepsgen(x, y, degree, numknot, seed = 5, stream = 0)
freepsgold(x, y, degree, numknot, seed = 5, stream = 0)
``` |

### Arguments

`x` |
A vector containing the values of the independent variable. |

`y` |
A vector containing the values of the dependent variable. |

`degree` |
The degree of the spline fit. |

`numknot` |
The number of knots. |

`seed` |
The value of the initial seed. Defaults to 5. |

`stream` |
The value of the initial stream to be used for parallel programming. Defaults to 0. |

### Value

An object of class "`freekt`

" containing the following components:

`x` |
A vector containing the x values. |

`y` |
A vector containing the y values. |

`degree` |
The degree of the spline fit. |

`seed` |
The value of the initial seed. |

`stream` |
The value of the stream. |

`lambda` |
The optimum amount of penalty. This is automatically equal to 0 for |

`optknot` |
A vector containing the optimal knots. |

`tracehat` |
The trace of the hat matrix for the optimal fit. |

`GCV` |
The value of generalized cross validation (GCV) for the optimal fit. |

`GSJS` |
The GSJS estimator, an estimator of the variance of the data. |

`call` |
The function call. |

### Author(s)

Steven Spiriti, Philip Smith, and Pierre Lecuyer

### References

Eubank, R. (1999), *Nonparametric Regression and Spline Smoothing*, New York: Marcel Dekker, Inc., Second ed.

Spiriti, S., Eubank, R., Smith, P., Young, D., "Knot Selection for Least-Squares and Penalized Splines," *Journal of Statistical Computation and Simulation*, in press.

### See Also

`fit.search.numknots`

for the case where the number of knots is not specified in advance.

### Examples

1 2 3 4 5 6 |