Testing the dilation order by using cumulative residual Tsallis entropy

In this paper, we introduce a new test for the dilation order based on cumulative residual Tsallis entropy of order α. The effect of the values of parameter α on the power of the test statistics is numerically investigated. The asymptotic distribution of the test statistic is given. The performance of the test statistic is evaluated using a simulation study. Finally, some numerical examples illustrating the theory are also given.     

基于股价预测的泛证券投资组合策略

本文基于期望效用最大化和L₁-中位数估计研究了在线投资组合选择问题。与EG（Exponential Gradient）策略仅利用单期价格信息估计价格趋势不同,本文将利用多期价格信息估计价格趋势,以提高在线策略的性能。首先,基于多期价格数据,利用L₁-中位数估计得到预期价格趋势。然后,通过期望效用最大化,提出一个新的具有线型时间复杂度的在线策略,EGLM（Exponential Gradient via L₁-Median）。并通过相对熵函数定义资产权重向量的距离,进而证明了EGLM策略具有泛证券投资组合性质。最后,利用国内外6个证券市场的历史数据进行实证分析,结果表明相较于UP（Universal Portfolio）策略和EG策略,EGLM策略有更好的竞争性能。     

基于未确知测度方法的城市化水平评价研究

城市化水平是一个国家和地区经济、社会、文化、科技水平的重要标志,也是衡量国家和地区社会组织程度和管理水平的重要标志。实施城市化战略,推进城市化进程,是我国逐步摆脱不发达状态,实现现代化历史任务的目标和手段的统一,也是21世纪初我国现代化建设中的重要任务。因此,做好城市化水平的评价工作对于一个地区的发展有着重要的战略意义。论文研究了信息熵和未确知测度方法在城市化水平评价中的应用,给出了综合评价模型,并结合实例进行验证分析。     

Interval censored and truncated data: Rate of convergence of NPMLE of the density

We consider survival data that are both interval censored and truncated. Under appropriate assumptions on the involved distributions, the censoring, truncation and survival, we prove the consistency of the NPMLE of the density of the survival, and give the rate of convergence. Finally, we give an example where the joint law of the censoring and truncation can be explicitly computed.     

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

Summary.  Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models , where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.     

Statistical analysis of dependent competing risks model in accelerated life testing under progressively hybrid censoring using copula function

This article considers statistical analysis of dependent competing risks model from Weibull distribution in accelerated life testing, in which copula function is used to examine the dependence structure between competing failure modes. We derive the maximum likelihood estimates, the approximate, and Bootstrap confidence intervals of the parameters. The effects of different dependence structures on the estimates of parameters are investigated. The simulation is given to compare the performance of the estimates when the competing failure modes are dependent with those when the failure modes are independent. Finally, one dataset was used for illustrative purpose in conclusion.     

Bivariate extension of (dynamic) cumulative past entropy

Recently, the concept of cumulative residual entropy (CRE) has been studied by many researchers in higher dimensions. In this article, we extend the definition of (dynamic) cumulative past entropy (DCPE), a dual measure of (dynamic) CRE, to bivariate setup and obtain some of its properties including bounds. We also look into the problem of extending DCPE for conditionally specified models. Several properties, including monotonicity, and bounds of DCPE are obtained for conditional distributions. It is shown that the proposed measure uniquely determines the distribution function. Moreover, we also propose a stochastic order based on this measure.     

Dynamic version of weighted cumulative residual entropy

Some extensions of Shannon entropy to the survival function have been recently proposed. Misagh et al. (2011 Misagh, F., Panahi, Y., Yari, G.H., Shahi, R. (2011, September). Weighted cumulative entropy and its estimation. In: Quality and Reliability (ICQR), 2011, IEEE International conference (pp. 477–480), IEEE.[Crossref] , [Google Scholar]) introduced weighted cumulative residual entropy (WCRE) that was studied more by Mirali et al. (2015 Mirali, M., Baratpour, S., Fakoor, V. (2015). On weighted cumulative residual entropy. Commun. Stat. Theory Methods. doi:10.1080103610926.2015.1053932.[Web of Science ®] , [Google Scholar]). In this article, the dynamic version of WCRE is proposed. Some relationships of this measure with well-known reliability measures and ageing classes are studied and some characterization results for exponential and Rayleigh distributions are provided. Also, a non parametric estimation of dynamic version of WCRE is introduced and its asymptotic behavior is investigated.     

Testing monotonic equilibrium residual entropy of N-State Random Evolution

In this study, we propose an information measure of uncertainty associated with the random equilibrium residual lifetime of a system driven by N-State Random Evolution. A U-statistic test driven by a moment inequality is proposed for testing the hypothesis that the uncertainty of equilibrium remaining life of a system remains unchanged (when system is in the steady state) against the alternative situation when system’s equilibrium residual life has increasing uncertainty over time (i.e., the life distribution has Increasing Equilibrium Residual Entropy property). Some numerical results such as tabulated critical values and empirical power of the proposed test statistic are presented as well.     

Goodness-of-fit tests based on Verma Kullback–Leibler information

In this article, a new consistent estimator of Veram’s entropy is introduced. We establish the entropy test based on the new information namely Verma Kullback–Leibler discrimination methodology. The results are used to introduce goodness-of-fit tests for normal and exponential distributions. The root of mean square errors, critical values, and powers for some alternatives are obtained by simulation. The proposed test is compared with other tests.