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Rates of Convergence in the Central Limit Theorem for Nonlinear Statistics Under Relaxed Moment Conditions

icon-email Nguyen Tien Dung

Abstract

This paper is concerned with normal approximation under relaxed moment conditions using Stein’s method. We obtain the explicit rates of convergence in the central limit theorem for (i) nonlinear statistics with finite absolute moment of order 2 + δ ∈ (2,3] and (ii) nonlinear statistics with vanishing third moment and finite absolute moment of order 3 + δ ∈ (3,4]. When applied to specific examples, these rates are of the optimal order O(n−δ2) and O(n−1+δ2). Our proofs are based on the covariance identity formula and simple observations about the solution of Stein’s equation.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Viện nghiên cứu cao cấp về toán Hội Toán học Mỹ MathScinet Thư viện số (VAST) Arxiv
Lịch hoạt động chung Lịch sử dụng phòng, hội trường, hội thảo Ảnh hoạt động
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Messages2TimelineExceptionsViews8RouteQueries108Models431MailsGateSessionRequest
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
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      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
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      Metadata
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