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Tail Estimation for Window-Censored Processes

Summary: [This abstract is based on the authors' 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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  • Topics: Software and Technology (for statistics, measurement, analysis), Statistics
  • Keywords: Generalized Pareto distribution, 100-Car naturalistic driving study, Length-biased distribution, Off-road glance, Tail estimation, Traffic safety
  • Author: Rootzén, Holger; Zholud, Dmitrii
  • Journal: Technometrics