Jonathan El Methni

Kernel estimation of extreme regression risk measures

The Regression Conditional Tail Moment (RCTM) is the risk measure defined as the moment of order b ≥ 0 of a loss distribution above the upper α-quantile where α ∈ (0, 1) and when a covariate information is available. The purpose of this work is first to establish the asymptotic properties of the RCTM in case of extreme losses, i.e when α → 0 is no longer fixed, under general extreme-value conditions on their distribution tail. In particular, no assumption is made on the sign of the associated extreme-value index. Second, the asymptotic normality of a kernel estimator of the RCTM is established, which allows to derive similar results for estimators of related risk measures such as the Regression Conditional Tail Expec-tation/Variance/Skewness. When the distribution tail is upper bounded, an application to frontier estimation is also proposed. The results are illustrated both on simulated data and on a real dataset in the field of nuclear reactors reliability.

Effects of Circadian Cortisol on the Development of a Health Habit.

Objective: Given the impact of individuals’ habits on health, it is important to study how behaviors can become habitual. Cortisol has been well documented to have a role in habit formation. This study aimed to elucidate the influence of the circadian rhythm of cortisol on habit formation in a real-life setting. Method: Forty-eight students were followed for 90 days during which they attempted to adopt a health behavior (psoas iliac stretch). They were randomly assigned to perform the stretch either upon waking in the morning, when cortisol concentrations are high, or before evening bedtime, when cortisol levels approach the nadir. A smartphone application was used to assess the Self-Report Behavioural Automaticity Index every day and to provide reminders for salivary measurements every 30 days. The speed of the health habit formation process was calculated by modeling the learning curves. Results: Extrapolation of the curves indicated that the morning group achieved automaticity at an earlier time point (105.95 days) than did the evening group (154.01 days). In addition, the cortisol level during the performance of the health behavior was identified as a significant mediator of the time point when the health behavior became habitual. Conclusion: The present findings suggest that the time course of the development of healthy habits depends on the time of the day and that the effect is mediated through diurnal variation in cortisol levels. Future studies are now needed to determine to what extent cortisol rhythmicity can help individuals to adopt new health behaviors.