### 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, 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 language | English (US) |
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Pages (from-to) | 925-932 |

Number of pages | 8 |

Journal | Econometric Theory |

Volume | 28 |

Issue number | 4 |

DOIs | |

State | Published - Aug 1 2012 |

### All Science Journal Classification (ASJC) codes

- Social Sciences (miscellaneous)
- Economics and Econometrics

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## Cite this

*Econometric Theory*,

*28*(4), 925-932. https://doi.org/10.1017/S0266466611000831