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Journal Articles Biometrical Journal Year : 2009

Improving point and interval estimators of monotone functions by rearrangement

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1
Victor Chernozhukov
  • Function : Author
Ivan Fernandez-Val
  • Function : Author
Alfred Galichon

Abstract

Suppose that a target function is monotonic and an available original estimate of this target function is not monotonic. Rearrangements, univariate and multivariate, transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function. Furthermore, suppose an original confidence interval, which covers the target function with probability at least 1-α, is defined by an upper and lower endpoint functions that are not monotonic. Then the rearranged confidence interval, defined by the rearranged upper and lower endpoint functions, is monotonic, shorter in length in common norms than the original interval, and covers the target function with probability at least 1-α. We illustrate the results with a growth chart example.
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Dates and versions

hal-03596970 , version 1 (04-03-2022)

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Victor Chernozhukov, Ivan Fernandez-Val, Alfred Galichon. Improving point and interval estimators of monotone functions by rearrangement. Biometrical Journal, 2009, 96 (3), pp.559 - 575. ⟨hal-03596970⟩
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