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Characterization of normal distribution related to two samples based on regression. (English) Zbl 1105.62015
Summary: Characterization of normal distributions related to two samples based on second conditional moments has been obtained. This characterization has been transformed to a characterization based on the UMVU estimators of the density function. These results are generalized to \(k\) samples from normal distributions. Finally, applications of these characterization results to goodness-of-fit test are discussed.
62E10 Characterization and structure theory of statistical distributions
62F03 Parametric hypothesis testing
62G10 Nonparametric hypothesis testing
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[1] D’Agostino RB, Stephens MA (1986) Goodness-of-fit techniques. Marcel Dekker, New York
[2] Gupta AK, Varga T (1990) Characterization of joint density by conditional densities. Commun. Statist. Theory Methods 19:4643–4652 · Zbl 0728.62016
[3] Gupta AK, Nguyen TT, Wang Y (1997) Characterizations of some continuous distributions. J Ital Statist Soc 1:59–65
[4] Lehmann EL, Casella G (1998) Theory of point estimation. Springer, Berlin Heidelberg New York · Zbl 0916.62017
[5] Nguyen TT, Dinh KT (1998) Characterizations of normal distributions supporting goodness-of-fit tests based on sample skewness and sample kurtosis. Metrika 48:21–30 · Zbl 0990.62008
[6] Nguyen TT, Dinh KT (2003) Characterizations of normal distributions and EDF goodness-of-fit tests. Metrika 58:149–157 · Zbl 1026.62010
[7] Rao CR (1967) On some characterizations of the normal law. Sankhya A 29:1–14 · Zbl 0158.37803
[8] Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Statist 23:470–472 · Zbl 0047.13104
[9] Singh J, Oliker VI (1979) On minimum variance unbiased estimation and characterization of densities. In: Proceedings of the Conference in Optical Methods in Statistics Academic, New York pp. 435–442 · Zbl 0458.62020
[10] Wang Y, Gupta AK, Nguyen TT (1996) Characterization theorems for some discrete distributions based on conditional structure. Can J Stat 24:257–262 · Zbl 0858.62008
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