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SOME EXTENSIONS OF A LEMMA OF KOTLARSKI

Published online by Cambridge University Press:  14 March 2012

Kirill Evdokimov  and
Halbert White
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Abstract

This note demonstrates that the conditions of Kotlarski’s (1967, Pacific Journal of Mathematics 20(1), 69–76) lemma can be substantially relaxed. In particular, the condition that the characteristic functions of M, U1, and U2 are nonvanishing can be replaced with much weaker conditions: The characteristic function of U1 can be allowed to have real zeros, as long as the derivative of its characteristic function at those points is not also zero; that of U2 can have an isolated number of zeros; and that of M need satisfy no restrictions on its zeros. We also show that Kotlarski’s lemma holds when the tails of U1 are no thicker than exponential, regardless of the zeros of the characteristic functions of U1, U2, or M.

Type
Brief Report
Information
Econometric Theory , Volume 28 , Issue 4 , August 2012 , pp. 925 - 932
Copyright
Copyright © Cambridge University Press 2012

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Footnotes

We thank Stéphane Bonhomme, Susanne Schennach, the editor, the co-editor, and two anonymous referees for helpful comments. Evdokimov gratefully acknowledges the support from the Gregory C. Chow Econometric Research Program at Princeton University.

References

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