Erratum to: Parameterizing mixture models with generalized moments

Abstract

1. In Sect. 3.1, the second sentence is “However since the error er (Q) depends on the unknown mixing distribution Q, instead we aim to minimize an upper bound of er (Q) instead.” The second “instead” should be deleted. 2. In Sect. 4.1, the first sentence below Definition 8 is “According to Caratheodory’s theorem, for each vector m ∈ conv( r+1), there exists a convex representation of m by {ui (θ)}i=0 with J < r + 1.” The less than sign in “J < r + 1” should be changed to the less than or equal to sign, i.e., “J ≤ r + 1”. 3. In Sect. 4.1, the second sentence below the second paragraph in Example 1 is “The boundary vectors of conv( 3) are either u(θ) ∈ R3 or (1−α)u(0)+αu(1), where 0 < α < 1.” Here “(1− α)u(0)+ αu(1)” should be changed to “(1− α)u(0)+ αu(25)”. 4. In Sect. 4.1, the third sentence of the second paragraph in Example 1 is “Therefore, the indexof a boundary vector is either 1 or 3/2; seeTheorem3.”Here “3/2” should be changed to “1/2”. 5. In Fig. 7, the axis labels in the panel (a) are u0 = 1, u1 = θ − 1, u2 = (θ − 1)2. The correct axis labels are u0(θ) = 1, u1 = (θ − 12.5) and u2 = (θ − 12.5)2; see Fig. 7.