On the unlinking conjecture of independent polynomial functions

Subir Kumar Bhandari and Ayanendranath Basu

Journal of Multivariate Analysis, 2006, vol. 97, issue 6, 1355-1360

Abstract: The celebrated U-conjecture states that under the Nn(0,In) distribution of the random vector X=(X1,...,Xn) in , two polynomials P(X) and Q(X) are unlinkable if they are independent [see Kagan et al., Characterization Problems in Mathematical Statistics, Wiley, New York, 1973]. Some results have been established in this direction, although the original conjecture is yet to be proved in generality. Here, we demonstrate that the conjecture is true in an important special case of the above, where P and Q are convex nonnegative polynomials with P(0)=0.

Keywords: Convex; polynomials; U-conjecture; Unlinkable; functions (search for similar items in EconPapers)
Date: 2006
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