Correction

This article refers to:

Improving Predictions When Interest Focuses on Extreme Random Effects

McCulloch, C. E., and Neuhaus, J. M. (2021), “Improving Predictions When Interests Focuses on Extreme Random Events,” Journal of the American Statistical Association, DOI: 10.1080/01621459.2021.1938583

JASA Correction

Equations (15)(15) $$\begin{array}{c}\text{numerator}\mathrm{}=\left(\mathrm{}-\sqrt{\frac{R}{1+R}}\varphi (A_{+})+\left[{\tilde{z}}_{BP}-\lambda \frac{R}{1+R}\right]\Phi (A_{+})\mathrm{}\right)e^{-\lambda {\tilde{z}}_{BP}}\\ +\left(\mathrm{}\sqrt{\frac{R}{1+R}}\varphi (A_{-})+\left[{\tilde{z}}_{BP}+\lambda \frac{R}{1+R}\right]\left[1-\Phi (A_{-})\right]\mathrm{}\right)e^{\lambda {\tilde{z}}_{BP}}\end{array}$$(15) and (16)(16) $$\text{denominator}\mathrm{}=e^{-\lambda {\tilde{z}}_{BP}}\Phi \left(A_{+}\right)+e^{\lambda {\tilde{z}}_{BP}}\left[1-\Phi (A_{-})\right],$$(16) in Section 4.5 and the definitions beneath them were incorrectly transcribed and should read as given below. The correct formulae were used in all the mean squared error of prediction calculations, so the results reported in the manuscript are correct.

Correction: When $w(z)=\hspace{0.17em}\text{exp}\hspace{0.17em}\left\{\lambda \right|z\left|\right\}$ the numerator and denominator of the optimal predictor, ${\tilde{z}}_{AB,\lambda },$ are, after some straightforward calculations, given by(15) $$\begin{array}{c}\text{numerator}\mathrm{}=\left(\mathrm{}-\sqrt{\frac{R}{1+R}}\varphi (A_{+})+\left[{\tilde{z}}_{BP}-\lambda \frac{R}{1+R}\right]\Phi (A_{+})\mathrm{}\right)e^{-\lambda {\tilde{z}}_{BP}}\\ +\left(\mathrm{}\sqrt{\frac{R}{1+R}}\varphi (A_{-})+\left[{\tilde{z}}_{BP}+\lambda \frac{R}{1+R}\right]\left[1-\Phi (A_{-})\right]\mathrm{}\right)e^{\lambda {\tilde{z}}_{BP}}\end{array}$$(15) (16) $$\text{denominator}\mathrm{}=e^{-\lambda {\tilde{z}}_{BP}}\Phi \left(A_{+}\right)+e^{\lambda {\tilde{z}}_{BP}}\left[1-\Phi (A_{-})\right],$$(16) where $A_{+}\equiv \left(\mathrm{}-{\tilde{z}}_{BP}+\lambda \frac{R}{1+R}\mathrm{}\right)\sqrt{\frac{1+R}{R}}$ and $A_{-}\equiv \left(\mathrm{}-{\tilde{z}}_{BP}-\lambda \frac{R}{1+R}\mathrm{}\right)\sqrt{\frac{1+R}{R}},$ and $\varphi (·)$ and $\Phi (·)$ are, respectively, the normal p.d.f. and c.d.f.