Trong bài báo này, chúng ta nghiên cứu bootstrap với kích thước Resample ngẫu nhiên mà không phải là độc lập của các mẫu ban đầu. Chúng tôi tìm thấy đủ điều kiện về kích thước Resample ngẫu nhiên cho các định lý giới hạn trung tâm để giữ cho mẫu bootstrap có nghĩa là. | Vietnam Journal of Mathematics 33. V Í e It ini ai m J o mt r im ai I of MATHEMATICS VAST 2005 On the Asymptotic Distribution of the Bootstrap Estimate with Random Resample Size Nguyen Van Toan Department of Mathematics College of Science Hue University 77 Nguyen Hue Hue Vietnam . Abstract. . . 1. Introduction . . . . . . . . . . . . . . This research is supported in part by the National Fundamental Research Program in Natural Science Vietnam No. 130701. Nguyen Van Toan . 1. . .-1. ._3 4. 2. Results n 1 . . . ._. . . . . 1. 2. . .1. Asymptotic Distribution of the Bootstrap Estimate with Random Resample Size i . . . . 2. .-1. . . . 1 2. .. . . . 1 . . . 1 2. 1 2. . . . n 1 tt . 1 tt. . . . . - - _ _ _ . Theorem . Let 1 X 2 . be a sequence of random variables on a probability mean and finite positive variance 2 Let be the empirical distribution of 1. Given 1. let 1. be conditionally independent random variables with common distribution and 1 be a sequence of positive integer valued random variables such that condition holds. Denote n e __ N n n -i2 - . -2 1 1 1 Along almost all sample sequences as tends to infinity tt oo N n 0 3. Proofs Lemma . .
