Abstract
The purpose of this paper is to show through three major examples from survival analysis, extreme value theory, and errors in variables that when it comes to statistical analysis, famous probabilistic results may lead to conceptual problems. As a consequence, we propose new approaches which may be of independent interest also in a probabilistic context.
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References
Balkema, A.A., De Haan, L.: Residual life time at great age. Ann. Probab. 2, 792–804 (1974)
Coles, S.: An Introduction to Statistical Modeling of Extreme Values. Springer, London (2001)
Dabrowska, D.M.: Kaplan–Meier estimate on the plane. Ann. Stat. 10, 1475–1489 (1988)
De Haan, L., Ferreira, A.: Extreme Value Theory, an Introduction. Springer, New York (2006)
Meister, A.: Deconvolution Problems in Nonparametric Statistics. Springer, Berlin Heidelberg (2009)
Prentice, R.L., Moodie, F., Wu, J.: Hazard-based nonparametric survivor function estimation. J. R. Stat. Soc. Ser. B: Stat. Methodol. 66, 305–319 (2004)
Resnick, S.I.: Extreme Values, Regular Variation and Point Processes. Springer, New York (2008)
Schennach, S.M.: Estimation of nonlinear models with measurement error. Econometrica 72, 33–75 (2004)
Sen, A., Stute, W.: Identification of survival functions through hazard functions in the Clayton-family. Stat. Probab. Lett. 87, 94–97 (2014)
Sen, A., Stute, W.: The multivariate Kaplan–Meier estimator (2019) (submitted for publication)
Stefanski, L.A., Carroll, R.J.: Deconvoluting Kernel density estimators. J. Theor. Appl. Stat. 21(2), 169–184 (1990)
Stute, W.: The central limit theorem under random censorship. Ann. Stat. 23, 422–439 (1995)
Stute, W., Wang, J.L.: The strong law under random censorship. Ann. Stat. 21, 1591–1607 (1993)
Subramanga, U.R.: On the max domains of attraction of univariate \(p\)-max stable laws. Stat. Probab. Lett. 19, 271–279 (1994)
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Stute, W. (2019). Stairway to Hell. In: Steland, A., Rafajłowicz, E., Okhrin, O. (eds) Stochastic Models, Statistics and Their Applications. SMSA 2019. Springer Proceedings in Mathematics & Statistics, vol 294. Springer, Cham. https://doi.org/10.1007/978-3-030-28665-1_1
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DOI: https://doi.org/10.1007/978-3-030-28665-1_1
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