We propose a new goodness-of-fit test for copulas, based on empirical copula processes and nonparametric bootstrap counterparts. The standard Kolmogorov-Smirnov type test for copulas that takes the supremum of the empirical copula process indexed by orthants is extended by test statistics based...

In this paper we discuss some statistical pitfalls that may occur in modeling cross-dependences with copulas in financial applications. In particular we focus on issues arising in the estimation and the empirical choice of copulas as well as in the design of time-dependent copulas

In this paper, we characterize explicitly the first derivative of the Value at Risk and the Expected Shortfall with respect to portfolio allocation when netting between positions exists. As a particular case, we examine a simple Gaussian example in order to illustrate the impact of netting...

Let X1,...,Xn be a sequence of i.i.d. random variables with common distribution P on the real line. Assuming that P has a smooth density, we construct a histogram based estimator Pn,H and establish weak convergence of the empirical process under sharp conditions. If is a class of indicators of...

In this thesis we establish that the blockwise bootstrap works for a large class of statistics. The main results are as follows: (i) A strongly mixing sequence satisfying the Central Limit Theorem for the mean, also satisfies the Moving Blocks Bootstrap Central Limit Theorem, in probability,...

We prove general theorems that characterize situations in which we could have asymptotic closeness between the original statistics Hn and its bootstrap version Hn∗, without stipulating the existence of weak limits. As one possible application we introduce a novel goodness of fit test based on...

It is shown that the blockwise bootstrap of the empirical process for a stationary [beta]-mixing sequences, indexed by VC-subgraph classes of functions, converges weakly to the appropriate Gaussian process, conditionally in probability. The conditions imposed are only marginally stronger than...

Dimitris Politis brought to my attention a typographic omission in the statement of Theorem 1. The block size b(n) should tend to infinity as n tends to infinity.

It is shown that if a strongly mixing sequence satisfies the Central Limit Theorem, then it also satisfies the Moving Blocks Bootstrap Central Limit Theorem in probability, even with bootstrapped norming. Regarding bootstrap in probability, this is the best possible result along the line of...