rk.prod {assist} | R Documentation |

## Calculate product of reproducing kernels

### Description

Return a matix as product of reproducing kernels

### Usage

```
rk.prod(x, ...)
```

### Arguments

`x` |
a matrix evaluating a reproducing kernel, or a vector. |

`...` |
optional lists of matrices evaluating reproducing kernels or vectors. All matrics must have the same dimensions. All vectors must have the same length. The length of each vector must equal to the column and row numbers of each matrix. |

### Details

The product of reproducing kernels is agian a reproducing kernel. In SS ANOVA, product of reproduing kernels is often used to model interaction spline terms.

### Value

a matrix as the product of reproducing kernels. If one argument is a vector, a `kron`

kernel is constructed first.

### Author(s)

Chunlei Ke chunlei_ke@yahoo.com and Yuedong Wang yuedong@pstat.ucsb.edu

### References

Gu, C. and Wahba, G. (1993a). Smoothing Spline ANOVA with component-wise Bayesian confidence intervals. Journal of Computational and Graphical Statistics 55, 353–368.

Gu, C. and Wahba, G. (1993b). Semiparametric analysis of variance with tensor product thin plate splines. JRSS B 55, 353–368.

### See Also

### Examples

```
## Not run:
x1<- 1:10/10
x2<- runif(10)
rk.prod(cubic(x1), periodic(x2))
## End(Not run)
```

*assist*version 3.1.9 Index]