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On an extension of a theorem of Linnik and Zinger

Published online by Cambridge University Press:  01 July 2016

Béla Gyires
Béla Gyires*
Affiliation:
Kossuth Lajos University, Debrecen, Hungary
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Abstract

In their paper [2] Linnik and Zinger proved a theorem which has an important role in both theoretical and applied statistics. For the proof of their theorem the authors used a condition which greatly narrows down its applicability. In this paper we prove the theorem of Linnik and Zinger without this condition, and also give other extensions of it.

Keywords

COMMON POLYNOMIAL STATISTICCONSTANT REGRESSIONENTIRE CHARACTERISTIC FUNCTION
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 4 , December 1975 , pp. 786 - 800
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Lukács, E. and Laha, R. G. (1964) Applications of Characteristic Functions. Hafner, New York.Google Scholar
[2] Zinger, A. A. and Linnik, Yu. V. (1957) On a class differential equation with an application to certain questions of regression theory. Vestnik Leningrad. Univ. 12, 121–130. (Translation in Selected Translations in Mathematical Statistics and Probability 2, 181–190, American Mathematical Society, Providence, R. I.) Google Scholar
[3] Zinger, A. A. (1958) Independence of quasi-polynomial statistics and analytic properties of distributions. Teor. Veroyatn. i. Primen. 3, 265–284. (Translation in Theor. Prob. Appl. 3, 247–268.) Google Scholar