Consistency of general bootstrap methods for degenerate -type and -type statistics

We provide general results on the consistency of certain bootstrap methods applied to degree-2 degenerate statistics of U-type and V-type. While it follows from well known results that the original statistic converges in distribution to a weighted sum of centred chi-squared random variables, we use a coupling idea of Dehling and Mikosch to show that the bootstrap counterpart converges to the same distribution. The result is applied to a goodness-of-fit test based on the empirical characteristic function.     

Multivariate process capability via Löwner ordering

Probability bounds can be derived for distributions whose covariance matrices are ordered with respect to Löwner partial ordering, a relation that is based on whether the difference between two matrices is positive definite. One example is Anderson’s Theorem. This paper develops a probability bound that follows from Anderson’s Theorem that is useful in the assessment of multivariate process capability. A statistical hypothesis test is also derived that allows one to test the null hypothesis that a given process is capable versus the alternative hypothesis that it is not capable on the basis of a sample of observed quality characteristic vectors from the process. It is argued that the proposed methodology is viable outside the multivariate normal model, where the p-value for the test can be computed using the bootstrap. The methods are demonstrated using example data, and the performance of the bootstrap approach is studied empirically using computer simulations.     

A parameterized approach to modeling and forecasting mortality

A new method is proposed of constructing mortality forecasts. This parameterized approach utilizes Generalized Linear Models (GLMs), based on heteroscedastic Poisson (non-additive) error structures, and using an orthonormal polynomial design matrix. Principal Component (PC) analysis is then applied to the cross-sectional fitted parameters. The produced model can be viewed either as a one-factor parameterized model where the time series are the fitted parameters, or as a principal component model, namely a log-bilinear hierarchical statistical association model of Goodman [Goodman, L.A., 1991. Measures, models, and graphical displays in the analysis of cross-classified data. J. Amer. Statist. Assoc. 86(416), 1085-1111] or equivalently as a generalized Lee-Carter model with p interaction terms. Mortality forecasts are obtained by applying dynamic linear regression models to the PCs. Two applications are presented: Sweden (1751-2006) and Greece (1957-2006).     

The uncertainties about the relationships risk–return–volatility in the Spanish stock market

The relationships between the market risk premium, its conditional variance and the risk-free rate in the Spanish stock market are studied in this paper. Using daily data, the above mentioned relations are analyzed by quasi maximum likelihood for an EGARCH-M(1,1) model with normal innovations and by nonparametric maximum likelihood for a semiparametric EGARCH-M(1,1) model with arbitrarily distributed innovations. It is worth mentioning that the conclusions differ from one model to the other.     

Analysis of the effects of the global financial crisis on the Turkish economy, using hierarchical methods

We have analyzed the topology of 50 important Turkish companies for the period 2006-2010 using the concept of hierarchical methods (the minimal spanning tree (MST) and hierarchical tree (HT)). We investigated the statistical reliability of links between companies in the MST by using the bootstrap technique. We also used the average linkage cluster analysis (ALCA) technique to observe the cluster structures much better. The MST and HT are known as useful tools to perceive and detect global structure, taxonomy, and hierarchy in financial data. We obtained four clusters of companies according to their proximity. We also observed that the Banks and Holdings cluster always forms in the centre of the MSTs for the periods 2006-2007, 2008, and 2009-2010. The clusters match nicely with their common production activities or their strong interrelationship. The effects of the Automobile sector increased after the global financial crisis due to the temporary incentives provided by the Turkish government. We find that Turkish companies were not very affected by the global financial crisis.     

参数法和非参数法估计组合样中被测组分含量的置信区间

本文以散装生铁块的随机样本分析结果为基础,应用Ｍｏｎｔｅ Ｃａｒｌｏ模拟法考察了组合样本中Ｓｉ、Ｍｎ,Ｃ,Ｓ,Ｐ含量（或份样平均值）的分布情况,研究了组分含量的置信区间,对参数法和非参数法的结果进行了比较。结果表明,对近似符合正态分布的原始总体或当组合样中的份样数目较多时,两种方法所估计的置信区间相近。但对偏离正态分布（或ｔ－分布）的总体且组合样中的份样数目较少时,非参数法较参数法的结果更符合实际     

两多维样本模型中位置参数相等性的M-检验

本文给出了基于投影寻踪方法检验两多维样本位置参数相等的M 统计量和t 统计量,分别用PP型自助M 统计量和PP型自助t 统计量给出了上述两统计量的近似分布, 并给出了检验的算法,进行一些模拟.     

System availability: Time dependence and statistical inference by (semi) non-parametric methods

Probability models are formulated for the availability (probability of being operative, i.e. not failed or down at fixed or random time t) of a variety of simple repairable systems. Single-exponential approximations of the time-dependent approach to long-run availability are presented. Problems of non-parametric estimation of time-dependent system availability from data are addressed by way of the empirical Laplace—Stieltjes transform. Uncertainty assessments are made by classical asymptotics (delta method) and by bootstrapping.     

指数族ACD模型的参数估计及其Bootstrap置信区间

针对指数族ACD模型,采用Scoring算法对模型进行参数估计,得到指数族情况下Scoring算法中方向向量的计算公式,并讨论了该算法的收敛性以及估计值的相合性.本文运用W ild Bootstrap构建参数的置信区间和置信带,将其结果与传统的残差Bootstrap做比较,数据模拟的结果表明,W ild Bootstrap处理问题更加快捷,结果更加准确.