一种简化的拟蒙特卡洛-高斯粒子滤波算法

提出了一种简化的拟蒙特卡洛-高斯粒子滤波（QMC-GPF）算法（SQMC-GPF）,以解决将QMC方法应用于GPF时计算复杂度高、运算量大的问题。该算法中，在连续的迭代滤波过程开始之前，首先利用QMC采样产生单位拟高斯分布粒子集，然后用其线性变换产生GPF算法中需要的高斯分布粒子集，省去了重新进行QMC采样步骤。该算法简化了新粒子集的产生过程，减少了运算量和滤波时间，增强了算法的实时性。将粒子滤波算法（PF）、GPF 算法、QMC-GPF算法和SQMC-GPF算法用于单变量非静态增长模型（UNGM）和二维纯角度跟踪模型（BOT）的仿真结果表明，SQMC-GPF算法的滤波性能与QMC-GPF算法的滤波性能相近，但有更为明显的速度优势，具有重要的实际应用价值。     

Are You All Normal? It Depends!

The assumption of normality has underlain much of the development of statistics, including spatial statistics, and many tests have been proposed. In this work, we focus on the multivariate setting and first review the recent advances in multivariate normality tests for i.i.d. data, with emphasis on the skewness and kurtosis approaches. We show through simulation studies that some of these tests cannot be used directly for testing normality of spatial data. We further review briefly the few existing univariate tests under dependence (time or space), and then propose a new multivariate normality test for spatial data by accounting for the spatial dependence. The new test utilises the union-intersection principle to decompose the null hypothesis into intersections of univariate normality hypotheses for projection data, and it rejects the multivariate normality if any individual hypothesis is rejected. The individual hypotheses for univariate normality are conducted using a Jarque–Bera type test statistic that accounts for the spatial dependence in the data. We also show in simulation studies that the new test has a good control of the type I error and a high empirical power, especially for large sample sizes. We further illustrate our test on bivariate wind data over the Arabian Peninsula.     

Thirty years on: A review of the Lee–Carter method for forecasting mortality

The introduction of the Lee–Carter (LC) method marked a breakthrough in mortality forecasting, providing a simple yet powerful data-driven stochastic approach. The method has the merit of capturing the dynamics of mortality change by a single time index that is almost invariably linear. This thirtieth anniversary review of its 1992 publication examines the LC method and the large body of research that it has since spawned. We first describe the method and present a 30-year ex post evaluation of the original LC forecast for U.S. mortality. We then review the most prominent extensions of the LC method in relation to the limitations that they sought to address. With a focus on the efficacy of the various extensions, we review existing evaluations and comparisons. To conclude, we juxtapose the two main statistical approaches used, discuss further issues, and identify several potential avenues for future research.