# davies.start: start value for Davies minimization routines In Davies: The Davies Quantile Function

## Description

Gives a “start” value for the optimization routines. Uses heuristics that seem to work.

## Usage

 `1` ```davies.start(x, threeps=c(0.1,0.5,0.9), small = 0.01) ```

## Arguments

 `x` dataset to be used `threeps` a three-element vector representing the quantiles to be balanced. The default values balance the first and ninth deciles and the median. These seem to work for me pretty well; YMMV `small` a “small” value to be used for lambda1 and lambda1 because using exactly zero is inappropriate

## Details

Returns a “start” value of the pararameters for use in one of the Davies fitting routines `maximum.likelihood()` or `least.squares()`.

Uses three heuristic methods (one assuming lambda1=lambda2, one with lambda1=0, and one with lambda2=0). Returns the best one of the three, as measured by `objective()`.

## Author(s)

Robin K. S. Hankin

`least.squares` , `maximum.likelihood`, `objective`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```d <- rchisq(40,1) davies.start(d) least.squares(d) params <- c(10 , 0.1 , -0.1) x <- rdavies(100 , params) davies.start(x) f <- function(threeps){objective(davies.start(x,threeps),x)} (jj<-optim(c(0.1,0.5,0.9),f)) davies.start(x,jj\$par) least.squares(x) #not bad at all. ```