On Local and Nonlocal Measures of Efficiency

Wilbert C.M. Kallenberg, Teresa Ledwina

Research output: Contribution to journalArticleAcademic

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Abstract

General results on the limiting equivalence of local and nonlocal measures of efficiency are obtained. Why equivalence occurs in so many testing and estimation problems is clarified. Uniformity of the convergence is a key point. The concepts of Frechet- and Hadamard-type differentiability, which imply uniformity, play an important role. The theory is applied to tests based on linear rank statistics, showing equivalence of the local limit of exact Bahadur efficiency and Pitman efficiency. As a second application, the relation between the inaccuracy rate and the asymptotic variance of $L$-estimators is investigated.
Original languageEnglish
Pages (from-to)1401-1420
JournalAnnals of statistics
Volume15
Issue number4
DOIs
Publication statusPublished - 1987

Fingerprint

Equivalence
Uniformity
L-estimators
Bahadur Efficiency
Pitman Efficiency
Linear Rank Statistics
Asymptotic Variance
Differentiability
Limiting
Imply
Testing
Concepts
Estimator
Asymptotic variance
Statistics

Keywords

  • IR-70376
  • $L$-estimators
  • inaccuracy rate
  • Exact Bahadur efficiency
  • linear rank statistics
  • Hadamard-type differentiability
  • Pitman efficiency
  • Large deviations
  • Frechet-type differentiability
  • Asymptotic variance

Cite this

Kallenberg, Wilbert C.M. ; Ledwina, Teresa. / On Local and Nonlocal Measures of Efficiency. In: Annals of statistics. 1987 ; Vol. 15, No. 4. pp. 1401-1420.
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Kallenberg, WCM & Ledwina, T 1987, 'On Local and Nonlocal Measures of Efficiency' Annals of statistics, vol. 15, no. 4, pp. 1401-1420. https://doi.org/10.1214/aos/1176350601

On Local and Nonlocal Measures of Efficiency. / Kallenberg, Wilbert C.M.; Ledwina, Teresa.

In: Annals of statistics, Vol. 15, No. 4, 1987, p. 1401-1420.

Research output: Contribution to journalArticleAcademic

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AU - Kallenberg, Wilbert C.M.

AU - Ledwina, Teresa

PY - 1987

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KW - IR-70376

KW - $L$-estimators

KW - inaccuracy rate

KW - Exact Bahadur efficiency

KW - linear rank statistics

KW - Hadamard-type differentiability

KW - Pitman efficiency

KW - Large deviations

KW - Frechet-type differentiability

KW - Asymptotic variance

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