kef {Conake} | R Documentation |

## Continuous associated kernel function

### Description

This function computes the discrete associated kernel function; see Chen (1999) and also Chen (2000).

### Usage

```
kef(x, t, h, ker, a = 0, b = 1)
```

### Arguments

`x` |
The target. |

`t` |
A single value or the grid where the continuous associated kernel function is computed. |

`h` |
The bandwidth or smoothing parameter. |

`ker` |
The associated kernel: "BE" extended beta, "GA" gamma, "LN" lognormal and "RIG" reciprocal inverse Gaussian. |

`a` |
The left bound of the support used for extended beta kernel. Default value is 0 for beta kernel. |

`b` |
The right bound of the support used for extended beta kernel. Default value is 1 for beta kernel. |

### Details

The associated kernel is one of the four which have been defined in the sections above : extended beta, gamma, lognormal and reciprocal inverse Gaussian; see Igarashi and Kakizawa (2015) and also Libengué (2013).

### Value

Returns the value of the discrete associated kernel function at t according to the target and the bandwidth.

### Author(s)

W. E. Wansouwé, F.G. Libengué and C. C. Kokonendji

### References

Chen, S. X. (1999). Beta kernels estimators for density functions, *Computational Statistics and Data Analysis* **31**, 131 - 145.

Chen, S. X. (2000). Gamma kernels estimators for density functions, *Annals of the Institute of Statistical Mathematics* **52**, 471 - 480.

Libengué, F.G. (2013).*Méthode Non-Paramétrique par Noyaux Associés Mixtes et Applications*, Ph.D. Thesis Manuscript (in French) to Université de Franche-Comté, Besançon, France and Université de Ouagadougou, Burkina Faso, June 2013, **LMB no. 14334**, Besançon.

Igarashi, G. and Kakizawa, Y. (2015). Bias correction for some asymmetric kernel estimators, *Journal of Statistical Planning and Inference* **159**, 37 - 63.

### Examples

```
x<-4
h<-0.1
t<-0:10
kef(x,t,h,"GA")
```

*Conake*version 1.0.1 Index]