Functional delta-method for the bootstrap of quasi-Hadamard differentiable functionals

The functional delta-method provides a convenient tool for deriving the asymptotic distribution of a plug-in estimator of a statistical functional from the asymptotic distribution of the respective empirical process. Moreover, it provides a tool to derive bootstrap consistency for plug-in estimators from bootstrap consistency of empirical processes. It has recently been shown that the range of applications of the functional delta-method for the asymptotic distribution can be considerably enlarged by employing the notion of quasi-Hadamard differentiability. Here we show in a general setting that this enlargement carries over to the bootstrap. That is, for quasi-Hadamard differentiable functionals bootstrap consistency of the plug-in estimator follows from bootstrap consistency of the respective empirical process. This enlargement often requires convergence in distribution of the bootstrapped empirical process w.r.t.\ a nonuniform sup-norm. The latter is not problematic as will be illustrated by means of examples

Continuous mapping approach to the asymptotics of UU- and VV-statistics

We derive a new representation for $U$- and $V$-statistics. Using this representation, the asymptotic distribution of $U$- and $V$-statistics can be derived by a direct application of the Continuous Mapping theorem. That novel approach not only encompasses most of the results on the asymptotic distribution known in literature, but also allows for the first time a unifying treatment of non-degenerate and degenerate $U$- and $V$-statistics. Moreover, it yields a new and powerful tool to derive the asymptotic distribution of very general $U$- and $V$-statistics based on long-memory sequences. This will be exemplified by several astonishing examples. In particular, we shall present examples where weak convergence of $U$- or $V$-statistics occurs at the rate $a_n^3$ and $a_n^4$, respectively, when $a_n$ is the rate of weak convergence of the empirical process. We also introduce the notion of asymptotic (non-) degeneracy which often appears in the presence of long-memory sequences.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ508 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

A Residual Bootstrap for Conditional Value-at-Risk

This paper proposes a fixed-design residual bootstrap method for the two-step estimator of Francq and Zako\"ian (2015) associated with the conditional Value-at-Risk. The bootstrap's consistency is proven for a general class of volatility models and intervals are constructed for the conditional Value-at-Risk. A simulation study reveals that the equal-tailed percentile bootstrap interval tends to fall short of its nominal value. In contrast, the reversed-tails bootstrap interval yields accurate coverage. We also compare the theoretically analyzed fixed-design bootstrap with the recursive-design bootstrap. It turns out that the fixed-design bootstrap performs equally well in terms of average coverage, yet leads on average to shorter intervals in smaller samples. An empirical application illustrates the interval estimation

Identifiability issues of age-period and age-period-cohort models of the Lee-Carter type

The predominant way of modelling mortality rates is the Lee-Carter model and its many extensions. The Lee-Carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that causes an inconsistent view on the latent variable. This paper considers identifiability issues of these models from a perspective that acknowledges the latent variable as a stochastic process from the beginning. We call this perspective the plug-in age-period or plug-in age-period-cohort model. Defining a parameter vector that includes the underlying parameters of this process rather than its realisations, we investigate whether the expected values and covariances of the plug-in Lee-Carter models are identifiable. It will be seen, for example, that even if in both steps of the estimation procedure we have identifiability in a certain sense it does not necessarily carry over to the plug-in models

Diagnostic study and meta-analysis of C-reactive protein as a predictor of postoperative inflammatory complications after gastroesophageal cancer surgery

Purpose: This study assessed the diagnostic accuracy of C-reactive protein (CRP) after gastroesophageal cancer resection for postoperative inflammatory complications (PIC). Methods: The clinical data and CRP values of patients operated on for gastroesophageal cancer surgery between 1997 and 2009 were retrospectively analyzed. The results of this study were compared with published data using a meta-analytic approach for diagnostic outcomes. Results: Of 210 patients included in the study, 59 developed PIC (28.1%; 95% CI: 22.5-34.5%). On the postoperative day (POD) 4 and 7, CRP had the best diagnostic accuracy for PIC (AUC 0.77; 95% CI, 0.64-0.91, AUC 0.81; 95% CI, 0.71-0.91). Using a cut-off value of 141mg/L (95% CI, 131-278mg/L) for CRP on POD 4, the sensitivity was 0.78 (95% CI, 0.55-0.91), the specificity was 0.70 (95% CI, 0.53-0.83) and the NPV was 0.89 (95% CI, 0.77-0.95). The in-hospital mortality rate was 3.3% (95% CI, 1.5-6.9%). In a diagnostic meta-analysis that included two additional studies, CRP had a significant predictive value after POD 3. Conclusion: There is limited evidence for the diagnostic accuracy of CRP levels for PIC after gastroesophageal cancer surgery. CRP levels on POD 4 might be useful to rule out PIC, but its diagnostic accuracy is moderate at best. For clinical routine use CRP levels are clearly not sufficient to predict PIC and have to be interpreted in the context of the whole clinical pictur