In biomedical studies, correlated failure time data arise often. Although point and confidence interval estimation for quantiles with independent censored failure time data have been extensively studied, estimation for quantiles with correlated failure time data has not been developed. In this article, we propose a nonparametric estimation method for quantiles with correlated failure time data....

− We address the estimation of quantiles from heavy-tailed distributions when functional covariate information is available and in the case where the order of the quantile converges to one as the sample size increases. Such ”extreme” quantiles can be located in the range of the data or near and even beyond the boundary of the sample, depending on the convergence rate of their order to one. Nonp...

This article proposes a simple approach to estimate quantiles of daily financial returns directly from high-frequency data. We denote the resulting estimator as realized quantile (RQ) and use it forecast tail risk measures, such Value at Risk (VaR) Expected Shortfall (ES). The RQ is built on assumption that logarithm prices are subordinated self-similar processes in intrinsic time. time dimensi...

M-estimators introduced in Huber (1964) provide a class of robust estimators of a center of symmetry of a symmetric probability distribution which also have very high eeciency at the model. However it is not clear what they do estimate when the probability distributions are nonsymmetric. In this paper we rst show that in the case of arbitrary, not necessarily symmetric probabilty distributions,...

Sample quantiles are consistent estimators for the true quantile and satisfy central limit theorems (CLTs) if the underlying distribution is continuous. If the distribution is discrete, the situation is much more delicate. In this case, sample quantiles are known to be not even consistent in general for the population quantiles. In a motivating example, we show that Efron’s bootstrap does not c...

We use bounds on the distribution function of the sum of two random variables with known marginal distributions obtained by Makarov (1981) to bound the distribution function of the individual treatment effect. Although the Makarov bounds are pointwise sharp if we only consider the marginals, they can be improved by using the fact that we know the mean (and only the mean) of the treatment effect...

In this thesis we investigate the analysis of energy-aware systems modeled by finitestate Markov chains. We deal with Markov chains augmented with transition weights and consider objectives referring to the accumulated weight along finite paths or to the quotient of the accumulated weight of two non-negative weight functions. Beside objectives asking for linear-time properties to be fulfilled w...