Tail Estimation for Window-Censored Processes |
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Authors: | Holger Rootzén Dmitrii Zholud |
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Affiliation: | 1. Mathematical Sciences, Chalmers and Gothenburg University SE-412 96 Gothenburg, Sweden (hrootzen@chalmers.se;2. dmitrii@chalmers.se) |
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Abstract: | This article develops methods to estimate the tail and full distribution of the lengths of the 0-intervals in a continuous time stationary ergodic stochastic process that takes the values 0 and 1 in alternating intervals. The setting is that each of many such 0–1 processes has been observed during a short time window. Thus, the observed 0-intervals could be noncensored, right-censored, left-censored, or doubly-censored, and the lengths of 0-intervals that are ongoing at the beginning of the observation window have a length-biased distribution. We exhibit parametric conditional maximum likelihood estimators for the full distribution, develop maximum likelihood tail estimation methods based on a semiparametric generalized Pareto model, and propose goodness-of-fit plots. Finite sample properties are studied by simulation, and asymptotic normality is established for the most important case. The methods are applied to estimation of the length of off-road glances in the 100-car study, a big naturalistic driving experiment. Supplementary materials that include MatLab code for the estimation routines and a simulation study are available online. |
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Keywords: | Generalized Pareto distribution 100-Car naturalistic driving study Length-biased distribution Off-road glance Tail estimation Traffic safety |
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