5,772 research outputs found

    Using a bootstrap method to choose the sample fraction in tail index estimation

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    Tail index estimation depends for its accuracy on a precise choice of the sample fraction, i.e. the number of extreme order statistics on which the estimation is based. A complete solution to the sample fraction selection is given by means of a two step subsample bootstrap method. This method adaptively determines the sample fraction that minimizes the asymptotic mean squared error. Unlike previous methods, prior knowledge of the second order parameter is not required. In addition, we are able to dispense with the need for a prior estimate of the tail index which already converges roughly at the optimal rate. The only arbitrary choice of parameters is the number of Monte Carlo replications.tail index;bias;bootstrap;mean squared error;optimal extreme sample fraction

    On functions with small differences

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    AbstractAn Abel-Tauber theorem is proved and applied to multiplicative arithmetic functions

    Differential trajectories of tobacco smoking in people at ultra-high risk for psychosis: Associations with clinical outcomes

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    Objective: People at ultra-high risk (UHR) for psychosis have a high prevalence of tobacco smoking, and rates are even higher among the subgroup that later develop a psychotic disorder. However, the longitudinal relationship between the course of tobacco smoking and clinical outcomes in UHR subjects is unknown.Ā Methods: We investigated associations between tobacco smoking and clinical outcomes in a prospective study of UHR individuals (n = 324). Latent class mixed model analyses were used to identify trajectories of smoking severity. Mixed effects models were applied to investigate associations between smoking trajectory class and the course of attenuated psychotic symptoms (APS) and affective symptoms, as assessed using the CAARMS.Ā Results: We identified four different classes of smoking trajectory: (i) Persistently High (n = 110), (ii) Decreasing (n = 29), (iii) Persistently Low (n = 165) and (iv) Increasing (n = 20). At two-year follow-up, there had been a greater increase in APS in the Persistently High class than for both the Persistently Low (ES = 9.77, SE = 4.87, p = 0.046) and Decreasing (ES = 18.18, SE = 7.61, p = 0.018) classes. There were no differences between smoking classes in the incidence of psychosis. There was a greater reduction in the severity of emotional disturbance and general symptoms in the Decreasing class than in the High (ES = āˆ’10.40, SE = 3.41, p = 0.003; ES = āˆ’22.36, SE = 10.07, p = 0.027), Increasing (ES = āˆ’11.35, SE = 4.55, p = 0.014; ES = āˆ’25.58, SE = 13.17, p = 0.050) and Low (ES = āˆ’11.38, SE = 3.29, p = 0.001; ES = āˆ’27.55, SE = 9.78, p = 0.005) classes, respectively.Ā Conclusions: These findings suggests that in UHR subjects persistent tobacco smoking is associated with an unfavorable course of psychotic symptoms, whereas decrease in the number of cigarettes smoked is associated with improvement in affective symptoms. Future research into smoking cessation interventions in the early stages of psychoses is required to shine light on the potential of modifying smoking behavior and its relation to clinical outcomes.</p
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