An approximation to the limit distribution of the epps-pulley test statistic for normality

Summary The approach of Epps and Pulley (1983) based on the empirical characteristic function is one of the most powerful tools for detecting any departures from normality. We obtain the first four moments of the limiting null distribution of the Epps-Pulley Statistic. Johnson- and Pearson curve fitting yields excellent approximations to simulated quantiles, and by modifying the test statistic the procedure may be carried out easily without the use of extensive tables for all sample sizes. Research done while the author was on leave at the University of Gie?en.     

A flexible model for actuarial risks under dependence

Methods for computing risk measures, such as stop-loss premiums, tacitly assume independence of the underlying individual risks. This can lead to huge errors even when only small dependencies occur. In the present paper, a general model is developed which covers what happens in practice in a realistic way. Moreover, it is also flexible, in the sense that it allows application in practice. Accurate and transparent approximations are presented, and the results obtained are illustrated through explicit examples.     

基于累积量的盲自适应波束形成技术

本文研究了在阵列信号处理中使用累积量的问题，以及在相干多径环境中基于累积量的盲自适应波束形成技术。该技术能在阵列几何结构和阵列流形未知的条件下，自适应调整权系数使阵列输出的信号干扰加噪声比最大。     

On Optimal Instrumental Variables Generators, with an Application to Hedge Fund Returns

In this paper, we propose a new benchmarking procedure lying on cumulants for computing the factor loadings in financial models of returns. We apply this technique to the well-known augmented Fama and French (J Fin Econ 43(2):153–193, 1997) model and compare it with another technique of ours based on higher moments. Our new procedure confirms the fact that the alpha is supposed to decrease when we disaggregate HFR indices to the level of individual funds while correcting for specification errors. Our new technique is therefore useful for hedge funds selection or ranking based on the alpha of Jensen corrected for specification errors. This technique will also be useful for calibrating other financial models of returns like the simple market model or the conditional alpha and beta models.

The Early History of the Cumulants and the Gram-Charlier Series

The early history of the Gram-Charlier series is discussed from three points of view: (1) a generalization of Laplace's central limit theorem, (2) a least squares approximation to a continuous function by means of Chebyshev-Hermite polynomials, (3) a generalization of Gauss's normal distribution to a system of skew distributions. Thiele defined the cumulants in terms of the moments, first by a recursion formula and later by an expansion of the logarithm of the moment generating function. He devised a differential operator which adjusts any cumulant to a desired value. His little known 1899 paper in Danish on the properties of the cumulants is translated into English in the Appendix.