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Fixed-width interval estimation of the minimum point of a regression function based on the Kiefer-Wolfowitz procedure

Authors
Journal
Journal of Statistical Planning and Inference
0378-3758
Publisher
Elsevier
Volume
30
Issue
3
Identifiers
DOI: 10.1016/0378-3758(92)90160-t
Keywords
  • Kiefer-Wolfowitz Procedure
  • Central Limit Theorem
  • Sequential Fixed-Width Interval Estimation
  • Asymptotic Consistency
  • Asymptotic Efficiency
  • Adaptive Procedure
Disciplines
  • Mathematics

Abstract

Abstract A version of the central limit theorem for the Kiefer-Wolfowitz procedure is stated. One constructs an asymptotically consistent fixed-width confidence interval for the minimum of a regression function. It is shown that the first moment of the corresponding stopping rule is finite. Both the construction and properties of the estimates of unknown parameters and an adaptive version of the procedure are presented.

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