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Erratum to: A Wald test with enhanced selectivity properties in homogeneous environments

The Original Article was published on 08 February 2013

After publication of our work [1] we noticed the following mistakes:

Equation (3) should be

$$ \boldsymbol{I}\left(\boldsymbol{\theta} \right)=\mathrm{E}\left[\left(\frac{\partial \ln f\left(\boldsymbol{x},\boldsymbol{X};\boldsymbol{\theta} \right)}{\partial {\boldsymbol{\theta}}^{*}}\right)\left(\frac{\partial \ln f\left(\boldsymbol{x},\boldsymbol{X};\boldsymbol{\theta} \right)}{\partial {\boldsymbol{\theta}}^T}\right)\right] $$
(3)

Equation (5) should be

$$ {t}_{\mathrm{Wald}}={\left({\widehat{\boldsymbol{\theta}}}_{r_1}-{\boldsymbol{\theta}}_{r_0}\right)}^H{\left\{{\left[{\boldsymbol{I}}^{-1}\left({\widehat{\boldsymbol{\theta}}}_1\right)\right]}_{{\boldsymbol{\theta}}_r{\boldsymbol{\theta}}_r^{*}}\right\}}^{-1}\left({\widehat{\boldsymbol{\theta}}}_{r_1}-{\boldsymbol{\theta}}_{r_0}\right) $$
(5)

The notation “--“ in equations (6), (11), and (12) should be replaced by “-“, i.e., the minus sign.

Equations (17), (18), and (19) should be

$$ {\tilde{t}}_{\mathrm{ACE}}=\frac{{\tilde{\boldsymbol{x}}}^H{\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}\tilde{\boldsymbol{x}}}{{\tilde{\boldsymbol{x}}}^H{\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}^{\perp}\tilde{\boldsymbol{x}}}=\frac{{\left\Vert {\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}\tilde{\boldsymbol{x}}\right\Vert}^2}{{\left\Vert {\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}^{\perp}\tilde{\boldsymbol{x}}\right\Vert}^2} $$
(17)
$$ {t}_{\mathrm{Wald}}=\frac{1}{1+{\left\Vert \tilde{\boldsymbol{x}}\right\Vert}^2{\left\Vert {\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}^{\perp}\tilde{\boldsymbol{x}}\right\Vert}^2/{\left\Vert {\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}\tilde{\boldsymbol{x}}\right\Vert}^2} $$
(18)

and

$$ {\tilde{t}}_{\mathrm{Wald}}=\frac{{\left\Vert {\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}\tilde{\boldsymbol{x}}\right\Vert}^2}{{\left\Vert {\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}^{\perp}\tilde{\boldsymbol{x}}\right\Vert}^2{\left\Vert \tilde{\boldsymbol{x}}\right\Vert}^2} $$
(19)

respectively.

References

  1. 1.

    W Liu, W Xie, Y Wang, A Wald test with enhanced selectivity properties in homogeneous environments. EURASIP J Adv Signal Process 2013, 14 (2013)

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Correspondence to Weijian Liu.

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The online version of the original article can be found under doi:10.1186/1687-6180-2013-14.

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Liu, W., Xie, W. & Wang, Y. Erratum to: A Wald test with enhanced selectivity properties in homogeneous environments. EURASIP J. Adv. Signal Process. 2015, 63 (2015). https://doi.org/10.1186/s13634-015-0252-8

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