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On the unlinking conjecture of independent polynomial functions


  • Bhandari, Subir Kumar
  • Basu, Ayanendranath


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.

Suggested Citation

  • Bhandari, Subir Kumar & Basu, Ayanendranath, 2006. "On the unlinking conjecture of independent polynomial functions," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1355-1360, July.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:6:p:1355-1360

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