We characterize second order regular variation of the tail sum of F together with a balance condition on the tails interms of the behaviour of the characteristic function near zero.

Asymptotic tail probabilities for bivariate linear combinations of subexponential random variables are given. These results are applied to explain the joint movements of the stocks of reinsurers. Portfolio investment and retrocession practices in the reinsurance industry, for reasons of...

It has been known for a long time that for bootstrapping the probability distribution of the maximum of a sample consistently, the bootstrap sample size needs to be of smaller order than the original sample size. See Jun Shao and Dongsheng Tu (1995), Ex. 3.9,p. 123. We show that the same is true...

We give a sufficient condition for i.i.d. random variables X1,X2 in order to have P{X1-X2>x} ~ P{|X1|>x} as x tends to infinity. A factorization property for subexponential distributions is used in the proof. In a subsequent paper the results will be applied to model fragility of financial markets.

For testing whether a distribution function is heavy tailed, we study the Kolmogorov test, Berk-Jones test, score test and their integrated versions. A comparison is conducted via Bahadur efficiency and simulations. The score test and the integrated score test show the best performance. Although...

Tail index estimation depends for its accuracy on a precise choice of the sample fraction, i.e. the number of extreme order statistics on which the estimation is based. A complete solution to the sample fraction selection is given by means of a two step subsample bootstrap method. This method...

Estimators of the extreme-value index are based on a set of upper order statistics. We present an adaptive method to choose the number of order statistics involved in an optimal way, balancing variance and bias components. Recently this has been achieved for the similar but somewhat less...

Experts often add domain knowledge to model-based forecasts while aiming to reduce forecast errors. Indeed, there is some empirical evidence that expert-adjusted forecasts improve forecast quality. However, surprisingly little is known about what experts actually do. Based on a large and...

This paper conjectures that the behaviour of experts who adjust statistical-model-based forecasts obeys the Law of Small Numbers [LSN]. To put this hypothesis to an empirical test, I propose a simple but effective methodology. It is applied to a database containing information on many experts...

The brand choice problem in marketing has recently been addressed with methods from computational intelligence such as neural networks. Another class of methods from computational intelligence, the so-called ensemble methods such as boosting and stacking have never been applied to the brand...