'Nonparametric inference in multivariate mixtures'<break/>Biometrika (2005), 92, pp. 667–678
The left-hand side of equation (2·8), on p. 671, should read {π<sub>1</sub> (1 − π<sub>1</sub>)}-super-−1/2 (2π<sub>1</sub> − 1) rather than {(1 − π<sub>1</sub>)/π<sub>1</sub>}-super-1/2 (2π<sub>1</sub> − 1). Reflecting this change, the left-hand side of equation (3·1) on the same page should be altered to <inline-formula><mml:math><mml:mrow><mml:mo stretchy="false">{</mml:mo><mml:msup><mml:mrow><mml:msub><mml:mrow><mml:mo ver><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mi>Ȣ 7;</mml:mi></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mn>1</mml:mn>< /mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml :msub><mml:mrow><mml:mover><mml:mrow><mml:mi>π</mml:mi></mml:mrow>< mml:mrow><mml:mi>∧</mml:mi></mml:mrow></mml:mover></mml:mrow><mml:m row><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">}</mml:mo></mml:mrow><mml:mrow><mml:mo>−</mml:mo>< mml:mn>1/2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mrow><mml:move r><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mi>∧ </mml:mi></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mn>1</mml:mn></m ml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula>, and the formula at the foot of p. 677 should be modified to {π<sub>1</sub> (1 − π<sub>1</sub>)}-super-−1/2 (2π<sub>1</sub> − 1) + O<sub>p</sub>(n-super-−1/2). No other formula is affected, and the left-hand side of (2·8) is still increasing in π<sub>1</sub>. The numerical results, discussed in §4, are influenced in minor ways. In the simulation study, absolute bias is reduced, and variance is either slightly increased or slightly decreased. In the real-data example, using the nonparametric approach to analysis, mean squared error is further reduced, from 0·0011 to 0·0004. We are grateful to Hiro Kasahara and Katsumi Shimotsu for pointing out the error. Copyright 2007, Oxford University Press.
