# Selection of the Tuning Parameter k

### Description

This function selects the tuning parameter k, the number of upper order statistics involved in Hill estimator of EVI among a grid of points following the method described in Section 3.3 of Wang and Li (2013). The method selects k as the value that minimizes the discrepancy between the estimated x-dependent EVI on the transformed scale and lam times the estimated x-dependent EVI on the original scale

### Usage

1 | ```
select.k.func(y, x, Lam.y, lam, a, max.tau, grid.k, n)
``` |

### Arguments

`y` |
a vector of n untransformed responses |

`x` |
a n x p matrix of n observations and p predictors |

`Lam.y` |
a vector of n power-transformed responses |

`lam` |
the power-transformation parameter |

`a` |
location shift parameter in the power transformation (introduced to avoid negative y values) |

`max.tau` |
the upper bound of the intermediate quantile levels |

`grid.k` |
the grid for the number of upper order statistics involved in Hill estimator |

`n` |
the number of observations |

### Value

the selected k is returned

### References

Wang, H. and Li, D. (2013). Estimation of conditional high quantiles through power transformation. Journal of the American Statistical Association, 108, 1062-1074.