HYPck

HYPck computes values of the scalars A, B, d for hyperbolic tangent estimator

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Syntax

Description

example

Anew =HYPck(c, k) Reconstuct columns 3:6 of Table 2 of HRR.

example

Anew =HYPck(c, k, A)

example

Anew =HYPck(c, k, A, B)

example

Anew =HYPck(c, k, A, B, d)

example

[Anew, Bnew] =HYPck(___)

example

[Anew, Bnew, d] =HYPck(___)

Examples

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  • Reconstuct columns 3:6 of Table 2 of HRR.

    • cc=3:6;
kk=4:0.5:5;
ABD=zeros(length(cc)*length(kk),4);
ij=1;
for c=cc
for k=kk
[A,B,d]=HYPck(c,k);
eff=B^2/A;
ABD(ij,:)=[A,B,d,eff];
ij=ij+1;
end
end

    Input Arguments

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    c — tuning constant c. Scalar.

    Scalar greater than 0 which controls the robustness/efficiency of the estimator

    Data Types: single| double

    k — sup of change of variance curve (CVC). Scalar.

    $k= supCVC(psi,x) x \in R$

    Data Types: single| double

    Optional Arguments

    A — A parameter. Scalar.

    Starting value for parameter A

    Example: 'A',0.85

    Data Types: double

    B — B parameter. Scalar.

    Starting value for parameter B

    Example: 'B',0.9

    Data Types: double

    d — d parameter. scalar.

    Starting value for parameter d

    Example: 'd',1,5

    Data Types: double

    Output Arguments

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    Anew —Value of parameter A. Scalar

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

    Bnew —Value of parameter B. Scalar

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

    d —Value of parameter d. Scalar

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

    More About

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    Additional Details

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

    References

    Hampel, F.R., Rousseeuw, P.J. and Ronchetti E. (1981), The Change-of-Variance Curve and Optimal Redescending M-Estimators, "Journal of the American Statistical Association", Vol. 76, pp. 643-648 [HRR]

    See Also

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