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Teoriya Veroyatnostei i ee Primeneniya, 1992, Volume 37, Issue 1, Pages 219–221 (Mi tvp4165)  

On the $Z$-Representation of a Statistic

R. J. Chau, F. J. Hu

National Tsing Hua University
Abstract: The usual way of presenting the departure of the standardized sample mean of independent and identically distributed random variables from a normal variable is to write its distribution as an expansion with the standard normal distribution function as its leading term and remainder terms of order $n^{ - 1/ 2} ,n^{ - 1}$ etc. An alternative representation, which reveals the departure by functions of the normal variable itself, is introduced. This representation is not unique when the dimensionality of the variables is not one. However, it is shown that different representations do not affect the distribution of functions of the sample mean.
English version:
Theory of Probability and its Applications, 1993, Volume 37, Issue 1, Pages 124–126
DOI: https://doi.org/10.1137/1137026
Bibliographic databases:
Language: Russian
Citation: R. J. Chau, F. J. Hu, “On the $Z$-Representation of a Statistic”, Teor. Veroyatnost. i Primenen., 37:1 (1992), 219–221; Theory Probab. Appl., 37:1 (1993), 124–126
Citation in format AMSBIB
\Bibitem{ChaHu92}
\by R.~J.~Chau, F.~J.~Hu
\paper On the $Z$-Representation of a Statistic
\jour Teor. Veroyatnost. i Primenen.
\yr 1992
\vol 37
\issue 1
\pages 219--221
\mathnet{http://mi.mathnet.ru/tvp4165}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1211239}
\transl
\jour Theory Probab. Appl.
\yr 1993
\vol 37
\issue 1
\pages 124--126
\crossref{https://doi.org/10.1137/1137026}
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    Теория вероятностей и ее применения Theory of Probability and its Applications
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