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A confidence interval for the slope of a truncated regression
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  • Published: March 1988

A confidence interval for the slope of a truncated regression

  • André Antille1 &
  • Philip Milasevic2 

Probability Theory and Related Fields volume 78, pages 63–72 (1988)Cite this article

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  • 2 Citations

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Summary

Bhattacharya, Chernoff and Yang (1983) proposed a nonparametric estimate for the slope of a regression lineY = β o X + V subjected to the truncationY≦y 0. The estimate corresponds to the zero-crossing of a random functionS n (β). In this paper an estimate for the asymptotic variance of the estimate of the slope is proposed and the rate of convergence is given. The proofs rest heavily on the local behavior ofS n (β) in the neighborhood of the true value βo.

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References

  1. Bhattacharya, P.K., Chernoff, H., Yang, S.S.: Nonparametric estimate of the slope of a truncated regression. Technical report no. 18, MIT (1980)

  2. Bhattacharya, P.K., Chernoff, H., Yang, S.S.: Nonparametric estimation of the slope of a truncated regression. Ann. Stat11, 505–514 (1983)

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  3. Billingsley, P.: Convergence of probability measures. New York: Wiley 1968

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  4. Milasevic, P.: Nonparametric estimation of the slope in the error-in-variables model. Preprint (1985)

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Author information

Authors and Affiliations

  1. Institut de Mathématiques, Université de Fribourg, CH-1700, Fribourg, Switzerland

    André Antille

  2. UER de Mathématiques, Faculté SSP, Université de Lausanne, CH-1015, Lausanne, Switzerland

    Philip Milasevic

Authors
  1. André Antille
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  2. Philip Milasevic
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Cite this article

Antille, A., Milasevic, P. A confidence interval for the slope of a truncated regression. Probab. Th. Rel. Fields 78, 63–72 (1988). https://doi.org/10.1007/BF00718035

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  • Received: 14 October 1985

  • Revised: 09 December 1987

  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF00718035

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Keywords

  • Confidence Interval
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Nonparametric Estimate
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