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.
References
Bhattacharya, P.K., Chernoff, H., Yang, S.S.: Nonparametric estimate of the slope of a truncated regression. Technical report no. 18, MIT (1980)
Bhattacharya, P.K., Chernoff, H., Yang, S.S.: Nonparametric estimation of the slope of a truncated regression. Ann. Stat11, 505–514 (1983)
Billingsley, P.: Convergence of probability measures. New York: Wiley 1968
Milasevic, P.: Nonparametric estimation of the slope in the error-in-variables model. Preprint (1985)
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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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DOI: https://doi.org/10.1007/BF00718035
Keywords
- Confidence Interval
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Nonparametric Estimate