A STOCHASTIC APPROXIMATION WITH A SEQUENCE OF DEPENDENT RANDOM VARIABLES

• 渡辺 正文

  福岡大学応用数学科

抄録

Let $ {Yn} $ be a sequence of dependent random variables and $ {Phi_n (cdot, cdot) } $ be a sequence of Borel functions. Let $ \theta_n $ be a solution of the equation $ M_n(x) = 0 $ for each $ n geqq 1 $, where $ M_n(x) = mathrm{E} Phi_n(x, Y_n) $. A Robbins-Monro type stochastic approximation procedure $ X_{n+1} = X_n - a_n Phi_n(X_n, Y_n) $ is considered for estimating $ \theta_n $ for $ n $ sufficiently large. Under some assumptions about $ {a_n},{\theta_n},{Y_n} $ and $ {Phi_n(cdot, cdot)} $ which may not include the fundamental condition $ mathrm{E}[Phi_n(X_n, Y_n) mid X_1, cdots, X_n] = M_n(X_n) $ a.s., the a.s. convergence and in mean-square convergence of $ mid X_n - \theta_n mid $ to zero are studied.

収録刊行物

• Bulletin of Mathematical Statistics

  Bulletin of Mathematical Statistics 19 (3/4), 25-42, 1981-03

  統計科学研究会

キーワード

• Industrial and Manufacturing Engineering
• General Agricultural and Biological Sciences
• General Business, Management and Accounting
• Materials Science (miscellaneous)
• Business and International Management

詳細情報

• CRID: 1390572174802471296
• NII論文ID: 120001036968
• NII書誌ID: AA00105332
• DOI: 10.5109/13146
• HANDLE: 2324/13146
• ISSN: 00074993
• 本文言語コード: en
• データソース種別:
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  • IRDB
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  • CiNii Articles
• 抄録ライセンスフラグ: 使用可