akj {quantreg} | R Documentation |

## Density estimation using adaptive kernel method

### Description

univariate adaptive kernel density estimation a la Silverman. As used
by Portnoy and Koenker (1989)

### Usage

akj(x, z, p, h, alpha, kappa, iker1, iker2)

### Arguments

`x` |
points used for centers of kernel assumed to be sorted |

`z` |
points at which density is calculated; default to seq( min(x), max(x), 2*length(x) ) |

`p` |
vector of probabilities associated with x's; default to 1/len(x) for each x. |

`h` |
initial window size (overall); default to Silverman's normal reference |

`alpha` |
a sensitivity parameter that determines the sensitivity of the local bandwidth to variations in the pilot density; default to .5 |

`kappa` |
constant determining initial (default) window width |

`iker1` |
kernel indicator, 0 for normal kernel (default) while 1 for cauchy kernel |

`iker2` |
xxx |

### Value

a R structure is returned

`dens` |
the vector of estimated density |

`psi` |
a vector of *psi=-f'/f* function |

`score` |
a vector of score *(f'/f)^2-f''/f* function |

`h` |
same as the input argument h |

### References

Portnoy, S and R Koenker, (1989) Adaptive L Estimation of Linear Models, Annals, 17, 362-81.
Silverman, B. (1986) Density Estimation, pp100-104.

[Package

*quantreg* version 3.82

Index]