# HAeff

HAeff finds the tuning constant that guarrantees a requested asymptotic efficiency

## Syntax

• ceff=HAeff(eff,v)example
• ceff=HAeff(eff,v,abc)example

## Description

 ceff =HAeff(eff, v) Find c for fixed efficiency.

 ceff =HAeff(eff, v, abc) Example where three input parameters are supplied.

## Examples

expand all

### Find c for fixed efficiency.

The constant c associated to a nominal location efficiency of 95% in regression is c = 0.690998716841394

c=HAeff(0.95,1)

### Example where three input parameters are supplied.

Find constant c associated to a nominal location efficiency of 95 per cent in regression when tun=[1.5,3.5,8].

tun=[1.5,3,8];
c=HAeff(0.95,1,tun);

## Input Arguments

### eff — efficiency. Scalar.

Scalar which contains the required efficiency (of location or scale estimator).

Generally eff=0.85, 0.9 or 0.95.

Data Types: single| double

### v — number of response variables. Scalar.

Number of variables of the dataset (for regression v=1) UP TO NOW v=1 (JUST REGRESSION) TO DO FOR MULTIVARIATE ANALYSIS

Data Types: single| double

### abc — parameters of Hampel estimator. Vector.

Vector of length 3 which contains the parameters of Hampel estimator. If vector abc is not specified it is set equal to [2, 4, 8]

Example: [1.5,3.5,8] 

Data Types: double

## Output Arguments

### ceff —Requested tuning constant. Scalar

Tuning constatnt of Hampel rho function associated to requested value of efficiency

Function HApsi transforms vector u as follows.

$HApsi(u) = \left\{ \begin{array}{cc} u & |u| <= a \\ a \times sign(u) & a <= |u| < b \\ a \frac{c-|u|}{c-b} \times sign(u) & b <= |u| < c \\ 0 & |u| >= c \end{array} \right.$

where $a$= ctun *param(1).

$b$= ctun *param(2).

$c$= ctun *param(3).

The default is $a$= 2*ctun.

$b$= 4*ctun.

$c$= 8*ctun.

It is necessary to have 0 <= a <= b <= c.

Parameter ctun multiplies parameters (a,b,c) of Hampel estimator.

## References

Hoaglin, D.C., Mosteller, F., Tukey, J.W. (1982), "Understanding Robust and Exploratory Data Analysis", Wiley, New York.