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...

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...

This paper introduces a minimum L1 distance estimate for parametric copula densities. It is shown that the expected L1 error of the estimate is within a given constant multiple of the best possible error plus an additive remainder term which is small under mild assumptions. The proof is based on...

We define a new approach to manage prepayment, default and interest rate risks simultaneously in some standard asset-backed securities structures. We propose a parsimonious top-down approach, by modeling directly the portfolio loss process and the amortization process. Both are correlated to...

We provide a rigorous proof of granularity adjustment (GA) formulas to evaluate loss distributions and risk measures (value-at-risk) in the case of heterogenous portfolios, multiple systematic factors and random recoveries. As a significant improvement with respect to the literature, we detail...

In competing risks model, several failure times arise potentially. The smallest failure time and its index only are observed. Without specific assumptions, the joint or even the marginal distribution functions of the underlying failure times are not identifiable (A. Tsiatis, Proc. Natl. Acad....