fitLS: Fitting splines with penalized least squares. In orthogonalsplinebasis: Orthogonal B-Spline Basis Functions

Description

Estimates the control vector for a spline fit by penalized least squares. The penalty being the penalty parameter times the functional inner product of the second derivative of the spline curve.

Usage

 `1` ```fitLS(object, x, y, penalty = 0) ```

Arguments

 `object` The SplineBasis object ot be used to make the fit `x` predictor variable. `y` response variable. `penalty` The penalty multiplier.

Details

For numeric vector y, and x, and a set of basis functions, represented in `object`, defined on the knots (k_0,…,k_m). The likelihood is defined by

sum_i (y_i-b(x_i)mu) + integral mu^T b''(t)^T b''(t) mu dt

The fucntion estimates μ.

Value

a vector of the control points.

Author(s)

Andrew Redd <aredd at stat.tamu.edu>

`SplineBasis`

Examples

 ```1 2 3 4 5``` ```knots<-c(0,0,0,0:5,5,5,5) base<-SplineBasis(knots) x<-seq(0,5,by=.5) y<-exp(x)+rnorm(length(x),sd=5) fitLS(base,x,y) ```

Example output

```Attaching package: 'orthogonalsplinebasis'

The following object is masked from 'package:stats':

integrate

[,1]
[1,]  -6.563343
[2,]  10.535190
[3,]  -5.904998
[4,]   2.957092
[5,]  13.036905
[6,]  62.784201
[7,]  88.525082
[8,] 148.675041
```

orthogonalsplinebasis documentation built on May 30, 2017, 5:21 a.m.