Functional Kernel Estimation of the Conditional Extreme Quantile under Random Right Censoring

The study of estimation of conditional extreme quantile in incomplete data frameworks is of growing interest. Specially, the estimation of the extreme value index in a censorship framework has been the purpose of many investigations when finite dimension covariate information has been considered. In this paper, the estimation of the conditional extreme quantile of a heavy-tailed distribution is discussed when some functional random covariate (i.e. valued in some infinite-dimensional space) information is available and the scalar response variable is right-censored. A Weissman-type estimator of conditional extreme quantiles is proposed and its asymptotic normality is established under mild assumptions. A simulation study is conducted to assess the finite-sample behavior of the proposed estimator and a comparison with two simple estimations strategies is provided.

Using Extreme Value Theory Approaches to Estimate High Quantiles for Stroke Data

This paper aims to explore the application of Extreme Value Theory (EVT) in estimating the conditional extreme quantile for time-to-event outcomes by examining the functional relationship between ambulatory blood pressure trajectories and clinical outcomes in stroke patients. The study utilizes EVT to analyze the functional connection between ambulatory blood pressure trajectories and clinical outcomes in a sample of 297 stroke patients. The 24-hour ambulatory blood pressure measurement curves for every 15 minutes are considered, acknowledging a censored rate of 40%. The findings reveal that the sample mean excess function exhibits a positive gradient above a specific threshold, confirming the heavy-tailed distribution of data in stroke patients with a positive extreme value index. Consequently, the estimated conditional extreme quantile indicates that stroke patients with higher blood pressure measurements face an elevated risk of recurrent stroke occurrence at an early stage. This research contributes to the understanding of the relationship between ambulatory blood pressure and recurrent stroke, providing valuable insights for clinical considerations and potential interventions in stroke management.

AN EFFICIENT SEQUENTIAL DESIGN FOR SENSITIVITY EXPERIMENTS

In sensitivity experiments, the response is binary and each experimental unit has a critical stimulus level that cannot be observed directly. It is often of interest to estimate extreme quantiles of the distribution of these critical stimulus levels over the tested products. For this purpose a new sequential scheme is proposed with some commonly used models. By using the bootstrap repeated-sampling principle, reasonable prior distributions based on a historic data set are specified. Then, a Bayesian strategy for the sequential procedure is provided and the estimator is given. Further, a high order approximation for such an estimator is explored and its consistency is proven. A simulation study shows that the proposed method gives superior performances over the existing methods.

Nonparametric Estimation of Extreme Conditional Quantiles with Functional Covariate

Estimation of the extreme conditional quantiles with functional covariate is an important problem in quantile regression. The existing methods, however, are only applicable for heavy-tailed distributions with a positive conditional tail index. In this paper, we propose a new framework for estimating the extreme conditional quantiles with functional covariate that combines the nonparametric modeling techniques and extreme value theory systematically. Our proposed method is widely applicable, no matter whether the conditional distribution of a response variable Y given a vector of functional covariates X is short, light or heavy-tailed. It thus enriches the existing literature.

SEQUENTIAL EMPIRICAL BAYESIAN DESIGN FOR SENSITIVITY EXPERIMENTS

Maximum likelihood recursions were used by Wu （1985） to estimate extreme quantiles of a quantal response curve. For certain choices of initial designs, Wu＇s method performs well. In many fields of application, there often exist some different initial designs which are known as the up-and- down designs. Based on the existing data set from such a design, the authors propose three sequential empirical Bayesian designs by quickly and efficiently exploiting the information in the testing data and known knowledge. The improvement obtained by using the new procedures for the estimation of extreme quantiles is substantial.