Notes and problems some extensions of a lemma of kotlarski

Kirill Evdokimov, Halbert White

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29 Scopus citations


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, U 1, and U 2 are nonvanishing can be replaced with much weaker conditions: The characteristic function of U 1 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 U 2 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 U 1 are no thicker than exponential, regardless of the zeros of the characteristic functions of U 1, U 2, or M.

Original languageEnglish (US)
Pages (from-to)925-932
Number of pages8
JournalEconometric Theory
Issue number4
StatePublished - Aug 2012

All Science Journal Classification (ASJC) codes

  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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