»ã±¨±êÌâ (Title)£ºCLT for high-dimensional R^2 statistics under a general independent components model (ͨ³£¶ÀÁ¢³É·ÖÄ£ÐÍϸßάR^2ͳ¼ÆÁ¿µÄCLT)

»ã±¨ÈË (Speaker)£ºÀîÎÀÃ÷ ³¤Æ¸¸±½ÌÊÚ£¨ÉϺ£²Æ¾­´óѧ£©

»ã±¨¹¦·ò (Time)£º2022Äê9ÔÂ4ÈÕ (ÖÜÈÕ) 13:30

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒ飨»áÒéºÅ£º385-558-280£©

Ô¼ÇëÈË(Inviter)£ºÕÅÑô´º

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»ã±¨ÌáÒª£ºThis paper establishes a central limit theorem (CLT) for R^2 statistics in a moderately high-dimensional asymptotic framework. The underlying population accommodates a general independent components model, by virtue of which our result unifies the two CLTs proposed separately in Zheng et al. (2014) and Guo and Cheng (2021). Beyond this, the new CLT demonstrates a non-negligible impact of kurtosis of the latent independent components on the fluctuation of R^2 statistics. As an application, a novel confidence interval is constructed for the coefficient of multiple correlation in a high-dimensional linear regression.