Convex rearrangements,generalized Lorenz curves,and correlated Gaussian data

We propose a statistical index for measuring the fluctuations of a stochastic process ξ$\xi$. This index is based on the generalized Lorenz curves and (modified) Gini indices of econometric theory.     

Analytic connections between a double design and its original design in terms of different optimality criteria

In recent years, there has been increasing interest in the study of double designs. Various popular optimality criteria have been proposed from different principles for design construction and comparison, such as E(s²), generalized minimum aberration (GMA), minimum moment aberration (MMA), and minimum projection uniformity (MPU). In this article, these criteria are reviewed, and analytic connections between a double design and its original design in terms of these criteria are investigated. These connections are suitable for general original two-level factorial design, whether regular or non regular. In addition, these results provide strong insight into the relationship between double design and original design from different viewpoints.     

Multilevel modelling of survey data: impact of the two-level weights used in the pseudolikelihood

Approaches that use the pseudolikelihood to perform multilevel modelling on survey data have been presented in the literature. To avoid biased estimates due to unequal selection probabilities, conditional weights can be introduced at each level. Less-biased estimators can also be obtained in a two-level linear model if the level-1 weights are scaled. In this paper, we studied several level-2 weights that can be introduced into the pseudolikelihood when the sampling design and the hierarchical structure of the multilevel model do not match. Two-level and three-level models were studied. The present work was motivated by a study that aims to estimate the contributions of lead sources to polluting the interior floor dust of the rooms within dwellings. We performed a simulation study using the real data collected from a French survey to achieve our objective. We conclude that it is preferable to use unweighted analyses or, at the most, to use conditional level-2 weights in a two-level or a three-level model. We state some warnings and make some recommendations.     

The minimum L2 distance estimator for Poisson mixture models

A robust estimator is developed for Poisson mixture models with a known number of components. The proposed estimator minimizes the L₂ distance between a sample of data and the model. When the component distributions are completely known, the estimators for the mixing proportions are in closed form. When the parameters for the component Poisson distributions are unknown, numerical methods are needed to calculate the estimators. Compared to the minimum Hellinger distance estimator, the minimum L₂ estimator can be less robust to extreme outliers, and often more robust to moderate outliers.     

On bivariate ageing properties of exchangeable Farlie–Gumbel–Morgenstern distributions

This paper deals with bivariate Farlie–Gumbel–Morgenstern distributions. We build the TP2 (RR2) property of the residual lifetime and study the evolution of the dependence of the residual lifetime at large age. Also, we derive the aging property in the sense of the upper orthant order. Furthermore, in the context of IFR (DFR) marginals the residual lifetime at the age above the median is found to be increasing (decreasing) in the upper orthant order.     

考虑随机利率和通货膨胀的连续时间资产组合选择

通过随机控制技术、Bellman最优性原理和HJB方程研究了通货膨胀、随机利率和交易成本等因素影响下的连续时间投资组合选择的最优化问题，将利率假定为服从Vasicek利率模型的随机过程，应用连续时间的动态均值-方差方法得到符合实际意义的HJB方程，通过多重网格的数值逼近方法求解相应的HJB方程得到双目标优化问题的最优投资策略。用实证方法与国内证券市场上代表性指数基金进行对比研究，发现通货膨胀和利率变动以及经济环境和投资者的异质信念等因素均会对最优策略产生影响，有效前沿会随之发生变化，债券与股票之间的投资比例并不是简单维持固定比例就可以保证总资产最优，拓展了基金分离定理。考虑通货膨胀和交易成本等因素的资产组合选择模型可以实实在在为机构投资者提供客观的实践指导和科学的理论依据。     

Extreme quantiles and tail index of a distribution based on kernel estimator

In this paper, we reveal the relationship between the tail exponent introduced by Parzen (1979) and tail index for a distribution function. Furthermore, we analyze the domain of attraction of the weighted sum of the distributions and its tail index. We show that the extreme quantiles can estimate directly, through knowing only the tail index of the kernel distribution function used in estimating the distribution function. Moreover, we give a smoothing parameter of extreme quantiles, which does not depend on any distribution function. The simulations and the application to reals data show that the proposed smoothed parameter gives better results for a heavy-tailed distribution, and for small sizes sample in extremes level.