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Uniformly Consistent Bootstrap Confidence Intervals: (English)

Uniformly Consistent Bootstrap Confidence Intervals: (English)

          
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About the Book

This dissertation, "Uniformly Consistent Bootstrap Confidence Intervals" by Zhuqing, Yu, 俞翥清, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: The bootstrap methods are widely used for constructing confidence intervals. However, the conventional bootstrap fails to be consistent under some nonstandard circumstances. The m out of n bootstrap is usually adopted to restore consistency, provided that a correct convergence rate can be specified for the plug-in estimators. In this thesis, we re-investigate the asymptotic properties of the bootstrap in a moving-parameter framework in which the underlying distribution is allowed to depend on n. We consider the problem of setting uniformly consistent confidence intervals for two non-regular cases: (1) the smooth function models with vanishing derivatives; and (2) the M-estimation with non-regular conditions. Under the moving-parameter setup, neither the conventional bootstrap nor the m out of n bootstrap is shown uniformly consistent over the whole parameter space. The results reflect to some extent finite-sample anomalies that cannot be explained by conventional, fixed-parameter, asymptotics. We propose a weighted bootstrap procedure for constructing uniformly consistent bootstrap confidence intervals, which does not require explicit specification of the convergence rate of the plug-in estimator. Under the smooth function models, we also propose a modified n out of n bootstrap procedure in special cases where the smooth function is applied to estimators that are uniformly bootstrappable. The estimating function bootstrap is also successfully employed for the latter model and enjoys computational advantages over the weighted bootstrap. We illustrate our findings by comparing the finite-sample coverage performances of the different bootstrap procedures. The stable performance of the proposed methods, contrasts sharply with the erratic coverages of the n out of n and m out of n bootstrap intervals, a result in agreement with our theoretical findings. DOI: 10.5353/th_b4775299 Subjects: Bootstrap (Statistics) Confidence intervals


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Product Details
  • ISBN-13: 9781361290392
  • Publisher: Open Dissertation Press
  • Publisher Imprint: Open Dissertation Press
  • Height: 279 mm
  • No of Pages: 118
  • Spine Width: 6 mm
  • Width: 216 mm
  • ISBN-10: 1361290390
  • Publisher Date: 26 Jan 2017
  • Binding: Paperback
  • Language: English
  • Series Title: English
  • Weight: 290 gr


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