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Some Extensions Of A Lemma Of Kotlarski

  • Evdokimov, Kirill
  • White, Halbert

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 .

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 28 (2012)
Issue (Month): 04 (August)
Pages: 925-932

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Handle: RePEc:cup:etheor:v:28:y:2012:i:04:p:925-932_00
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  1. Stéphane Bonhomme & Jean-Marc Robin, 2008. "Generalized nonparametric deconvolution with an application to earnings dynamics," CeMMAP working papers CWP03/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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