Bootstrapping Nonparametric Prediction Intervals for Conditional Value-at-Risk with Heteroscedasticity

Using bootstrap method, we have constructed nonparametric prediction intervals for Conditional Value-at-Risk for returns that admit a heteroscedastic location-scale model where the location and scale functions are smooth, and the function of the error term is unknown and is assumed to be uncorrelated to the independent variable. The prediction interval performs well for large sample sizes and is relatively small, which is consistent with what is obtainable in the literature.

Adaptive parametric prediction of event times in clinical trials

Background: In event-based clinical trials, it is common to conduct interim analyses at planned landmark event counts. Accurate prediction of the timing of these events can support logistical planning and the efficient allocation of resources. As the trial progresses, one may wish to use the accumulating data to refine predictions. Purpose: Available methods to predict event times include parametric cure and non-cure models and a nonparametric approach involving Bayesian bootstrap simulation. The parametric methods work well when their underlying assumptions are met, and the nonparametric method gives calibrated but inefficient predictions across a range of true models. In the early stages of a trial, when predictions have high marginal value, it is difficult to infer the form of the underlying model. We seek to develop a method that will adaptively identify the best-fitting model and use it to create robust predictions. Methods: At each prediction time, we repeat the following steps: (1) resample the data; (2) identify, from among a set of candidate models, the one with the highest posterior probability; and (3) sample from the predictive posterior of the data under the selected model. Results: A Monte Carlo study demonstrates that the adaptive method produces prediction intervals whose coverage is robust within the family of selected models. The intervals are generally wider than those produced assuming the correct model, but narrower than nonparametric prediction intervals. We demonstrate our method with applications to two completed trials: The International Chronic Granulomatous Disease study and Radiation Therapy Oncology Group trial 0129. Limitations: Intervals produced under any method can be badly calibrated when the sample size is small and unhelpfully wide when predicting the remote future. Early predictions can be inaccurate if there are changes in enrollment practices or trends in survival. Conclusions: An adaptive event-time prediction method that selects the model given the available data can give improved robustness compared to methods based on less flexible parametric models.

Nonparametric Prediction Intervals of generalized order statistics from two independent sequences

<p>This paper, discusses the problem of predicting future a generalized order statistic of an iid sequence sample was drawn from an arbitrary unknown distribution, based on observed also generalized order statistics from the same population. The coverage probabilities of these prediction intervals are exact and free of the parent distribution F(). Prediction formulas of ordinary order statistics and upper record values are extracted as special cases from the productive results. Finally, numerical computations on several models of ordered random variables are given to illustrate the proposed procedures.</p>