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General saddlepoint approximations to distributions under an elliptical population |
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| Authors: | Takahiro Tsuchiya Sadanori Konishi |
| Institution: | 1. The Institutt of Statistical Mathematics , 4-6-7 Mmami-Azaku, Minato-hi, Tokyo, 106-8569, Japan;2. Graduate School of Mathematics , Kyushu Umccisily , 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan |
| Abstract: | General saddlepoint approximations are derived for the distributions of statistics under an elliptical population. The technique is applied to obtain the tail probabilities of latent roots of a sample covariance matrix. It is shown that the method based on normalizing transformations by Tsuchiya and Konishi (1997) is efficient for the sample correlation coefficient in an elliptical sample. |
| Keywords: | approximate cumulant generating Junction notnial-izinq transformations tail probabilities latent root: sample covariance matrix sample conrdatioii Lutfficitrtt coefficient of variation |