Least squares theory for possibly singular models

In a recent paper, Scobey (1975) observed that the usual least squares theory can be applied even when the covariance matrix σ²V of Y in the linear model Y = Xβ + e is singular by choosing the Moore-Penrose inverse (V+XX′)⁺ instead of V^-1 when V is nonsingular. This result appears to be wrong. The appropriate treatment of the problem in the singular case is described.     

离散复镜像理论对近地电偶极子的应用

对近地电偶极子赫芝矢位中的索末菲积分,仅用 Prony 法,对其被积函数分式部分进行指数函数逼近,可得到近地电偶极子的一串离散镜像,而这类积分就可看作这些镜像在观察点的解。采用此方法大大节省了计算时间,所得结果与沿实轴数值积分结果吻合很好。对索末菲积分在实轴上可能遇到的奇异点,采用分部积分法消去之,避免了给数值积分带来的麻烦。     

Multivariate hypothesis testing using generalized and {2}-inverses – with applications

The use of generalized inverses in Wald's-type quadratic forms of test statistics having singular normal limiting distributions does not guarantee to obtain chi-square limiting distributions. In this article, the use of {2} -inverses for that problem is investigated. Alternatively, Imhof-based test statistics can also be defined, which converge in distribution to weighted sum of chi-square variables. The asymptotic distributions of these test statistics under the null and alternative hypotheses are discussed. Under fixed and local alternatives, the asymptotic powers are compared theoretically. Simulation studies are also performed to compare the exact powers of the test statistics in finite samples. A data analysis on the temperature and precipitation variability in the European Alps illustrates the proposed methods.     

Randomized singular spectrum analysis for long time series

ABSTRACT

Singular spectrum analysis (SSA) is a relatively new method for time series analysis and comes as a non-parametric alternative to the classical methods. This methodology has proven to be effective in analysing non-stationary and complex time series since it is a non-parametric method and do not require the classical assumptions over the stationarity or over the normality of the residuals. Although SSA have proved to provide advantages over traditional methods, the challenges that arise when long time series are considered, make the standard SSA very demanding computationally and often not suitable. In this paper we propose the randomized SSA which is an alternative to SSA for long time series without losing the quality of the analysis. The SSA and the randomized SSA are compared in terms of quality of the model fit and forecasting, and computational time. This is done by using Monte Carlo simulations and real data about the daily prices of five of the major world commodities.     

奇导协方差矩阵和任意收益率分布下均值-CVaR模型的有效边界特征

本文利用现代主流风险度量技术CVaR代替方差或VaR,建立了均值-CVaR模型,在任意收益率分布下,利用无套利均衡分析的方法研究了奇异协方差矩阵情形的投资组合问题,得到了模型有效边界的本质特征,最后作为结论的直接应用和说明,我们给出了一个具体的算例分析。     

关于实质条件句的两个问题

实质条件句和蕴涵的关系如何？实质条件句与日常语言中的条件句的关系如何？这是关于实质条件句的两个基本问题。澄清了实质条件句和蕴涵的关系，指出不能将蕴涵混同于相应的实质条件句的真理性，并在此基础上分析了所谓的蕴涵悖论。应该将实质条件句在技术上的价值与它在日常语言中的对应物这两个问题分开处理，并论证了以实质条件句概念解释日常语言中的直陈单独条件句的适当性，指出两者之间的关系是卡尔纳普所谓之辩明关系。     

A new reproducing kernel-based nonlinear dimension reduction method for survival data

Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS-based Double SIR) to nonlinear dimension reduction for survival data is proposed. An isometric isomorphism is constructed based on the RKHS property, then the nonlinear function in the RKHS can be represented by the inner product of two elements that reside in the isomorphic feature space. Due to the censorship of survival data, double slicing is used to estimate the weight function to adjust for the censoring bias. The nonlinear sufficient dimension reduction (SDR) subspace is estimated by a generalized eigen-decomposition problem. The asymptotic property of the estimator is established based on the perturbation theory. Finally, the performance of RDSIR is illustrated on simulated and real data. The numerical results show that RDSIR is comparable with the linear SDR method. Most importantly, RDSIR can also effectively extract nonlinearity from survival data.     

基于滚动时间窗的碳市场价格分解集成预测研究

提高碳市场价格预测准确性对于交易风险监测以及碳市场平稳发展具有重要价值。针对复杂的、非线性碳市场价格数据的短期预测误差偏大、分解过程易产生数据泄露问题，提出了基于滚动时间窗的SSA-SVR分解集成预测框架。首先，选取时间窗数据，继而借助奇异谱分析将时间窗内碳价序列分解重构为高、低频序列；然后，使用支持向量回归方法对高、低频序列分别进行预测；最后，加和集成预测结果，得到下一时刻的碳市场价格预测值。通过不断更新时间窗的数据内容，动态执行“分解-预测-集成”过程，实现碳市场价格的实时预测。研究结果表明，本文所提出框架表现出优异且稳定的预测性能，在碳市场价格预测研究中具有良好的适用性和有效性。