# HYPeff

HYPeff finds constant c which is associated to the requested efficiency for hyperbolic estimator

## Syntax

• c=HYPeff(eff, v)example
• c=HYPeff(eff, v, k)example
• c=HYPeff(eff, v, k, traceiter)example
• [c,A]=HYPeff(___)example
• [c,A,B]=HYPeff(___)example
• [c,A,B,d]=HYPeff(___)example

## Description

 c =HYPeff(eff, v) Find parameters for fixed efficiency and k.

 c =HYPeff(eff, v, k) Example of use of option Find parameters for fixed efficiency and k.

 c =HYPeff(eff, v, k, traceiter)

 [c, A] =HYPeff(___)

 [c, A, B] =HYPeff(___)

 [c, A, B, d] =HYPeff(___)

## Examples

expand all

### Find parameters for fixed efficiency and k.

Find value of c, A, B, for a nominal efficiency of 0.8427 when k=4.5

ktuning=4.5;
[c,A,B,d]=HYPeff(0.8427,1,ktuning);
% In this case
% c = 3.000130564905703
% A = 0.604298601602487
% B = 0.713612241773758
% d= 1.304379168746527
% See also Table 2 of HRR p. 645

### Example of use of option Find parameters for fixed efficiency and k.

Find value of c, A, B, for a nominal efficiency of 0.8427 when k=4.5

ktuning=4.5;
traceiter =true;
[c,A,B,d]=HYPeff(0.8427,1,ktuning,traceiter);
% In this case
% c = 3.000130564905703
% A = 0.604298601602487
% B = 0.713612241773758
% d= 1.304379168746527
% See also Table 2 of HRR p. 645

## 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

### k — supremum of the change of variance curve. Scalar.

$\sup CVC(psi,x) x \in R$ Default value is k=4.5.

Example: 'k',5 

Data Types: double

### traceiter — Level of display. Scalar.

If traceiter = 1 it is possible to monitor how the value of the objective function B^2/A gets closer to the target (eff) during the iterations

Example: 'traceiter',0 

Data Types: double

## Output Arguments

### c —parameter c of hyperbolic tangent estimator. Scalar

For more details see the methodological details inside "More About" below

### A —parameter A of hyperbolic tangent estimator. Scalar

For more details see the methodological details inside "More About" below

### B —parameter B of hyperbolic tangent estimator. Scalar

For more details see the methodological details inside "More About" below

### d —parameter d of hyperbolic tangent estimator. Scalar

For more details see the methodological details inside "More About" below

$HYPpsi(u) = \left\{ \begin{array}{cc} u & |u| \leq d \\ \sqrt{A (k - 1)} \tanh \left( \sqrt{(k - 1) B^2/A} (c -|u|)/2 \right) sign(u) & d \leq |u| < c, \\ 0 & |u| \geq c. \end{array} \right.$ It is necessary to have $0 < A < B < 2 normcdf(c)-1- 2 c \times normpdf(c) <1$