Characterization of normal distribution related to two samples based on regression.

*(English)*Zbl 1105.62015Summary: 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.

##### MSC:

62E10 | Characterization and structure theory of statistical distributions |

62F03 | Parametric hypothesis testing |

62G10 | Nonparametric hypothesis testing |

##### Keywords:

UMVUE of the density function; Characteristic function; Differential equation; Moment; Empirical distribution function
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##### References:

[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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