Sparse Approximations of Fractional Matérn Fields

We consider fast lattice approximation methods for a solution of a certain stochastic non‐local pseudodifferential operator equation. This equation defines a Matérn class random field. We approximate the pseudodifferential operator with truncated Taylor expansion, spectral domain error functional minimization and rounding approximations. This allows us to construct Gaussian Markov random field approximations. We construct lattice approximations with finite‐difference methods. We show that the solutions can be constructed with overdetermined systems of stochastic matrix equations with sparse matrices, and we solve the system of equations with a sparse Cholesky decomposition. We consider convergence of the truncated Taylor approximation by studying band‐limited Matérn fields. We consider the convergence of the discrete approximations to the continuous limits. Finally, we study numerically the accuracy of different approximation methods with an interpolation problem.     

Three strings of inequalities among six Bayes estimators

We discover three interesting strings of inequalities among six Bayes estimators, where for the parameter space (0, 1), (0, ∞), and ( ? ∞, ∞), each case has a string of inequalities. The three strings of inequalities only depend on the loss functions, and the inequalities are independent of the chosen models and the used priors provided the Bayes estimators exist. Therefore, they exist in a general setting which makes them quite interesting. Finally, the numerical simulations exemplify the two strings of inequalities defined on (0, 1) and (0, ∞), and that there does not exist a string of inequalities among the six smallest posterior expected losses.     

A simple,doubly robust,efficient estimator for survival functions using pseudo observations

Survival functions are often estimated by nonparametric estimators such as the Kaplan‐Meier estimator. For valid estimation, proper adjustment for confounding factors is needed when treatment assignment may depend on confounding factors. Inverse probability weighting is a commonly used approach, especially when there is a large number of potential confounders to adjust for. Direct adjustment may also be used if the relationship between the time‐to‐event and all confounders can be modeled. However, either approach requires a correctly specified model for the relationship between confounders and treatment allocation or between confounders and the time‐to‐event. We propose a pseudo‐observation–based doubly robust estimator, which is valid when either the treatment allocation model or the time‐to‐event model is correctly specified and is generally more efficient than the inverse probability weighting approach. The approach can be easily implemented using standard software. A simulation study was conducted to evaluate this approach under a number of scenarios, and the results are presented and discussed. The results confirm robustness and efficiency of the proposed approach. A real data example is also provided for illustration.     

The economic impact of prolonged political instability: a case study of Fiji

It has been long believed that prolonged political instability harms economic growth and development. This paper contributes to this growing empirical literature by studying the case in Fiji, which has faced a long period of political instability caused by a series of coups, military administrations and frequent changes in government since 1987. The impact of political instability on growth is hard to identify empirically because the counterfactual is unobserved and it is difficult to find valid comparisons. To solve this problem, we use the recently developed Synthetic Control Method to construct a counterfactual (or synthetic Fiji) that predicts the growth of a politically stable Fiji. The difference in per capita growth trajectories of the synthetic and the actual Fiji can thus be attributed as the impacts of political instability. Our findings show that the political instability caused by a series of coups since 1987 has indeed led Fiji onto a lower growth path, and that the accumulated effect is getting larger.     

Estimation of Stratified Mark‐Specific Proportional Hazards Models with Missing Marks

Abstract. An objective of randomized placebo‐controlled preventive HIV vaccine efficacy trials is to assess the relationship between the vaccine effect to prevent infection and the genetic distance of the exposing HIV to the HIV strain represented in the vaccine construct. Motivated by this objective, recently a mark‐specific proportional hazards (PH) model with a continuum of competing risks has been studied, where the genetic distance of the transmitting strain is the continuous ‘mark’ defined and observable only in failures. A high percentage of genetic marks of interest may be missing for a variety of reasons, predominantly because rapid evolution of HIV sequences after transmission before a blood sample is drawn from which HIV sequences are measured. This research investigates the stratified mark‐specific PH model with missing marks where the baseline functions may vary with strata. We develop two consistent estimation approaches, the first based on the inverse probability weighted complete‐case (IPW) technique, and the second based on augmenting the IPW estimator by incorporating auxiliary information predictive of the mark. We investigate the asymptotic properties and finite‐sample performance of the two estimators, and show that the augmented IPW estimator, which satisfies a double robustness property, is more efficient.     

Regularized Posteriors in Linear Ill‐Posed Inverse Problems

Abstract. We study the Bayesian solution of a linear inverse problem in a separable Hilbert space setting with Gaussian prior and noise distribution. Our contribution is to propose a new Bayes estimator which is a linear and continuous estimator on the whole space and is stronger than the mean of the exact Gaussian posterior distribution which is only defined as a measurable linear transformation. Our estimator is the mean of a slightly modified posterior distribution called regularized posterior distribution. Frequentist consistency of our estimator and of the regularized posterior distribution is proved. A Monte Carlo study and an application to real data confirm good small‐sample properties of our procedure.     

Proportional hazards model for competing risks data with missing cause of failure

We consider the semiparametric proportional hazards model for the cause-specific hazard function in analysis of competing risks data with missing cause of failure. The inverse probability weighted equation and augmented inverse probability weighted equation are proposed for estimating the regression parameters in the model, and their theoretical properties are established for inference. Simulation studies demonstrate that the augmented inverse probability weighted estimator is doubly robust and the proposed method is appropriate for practical use. The simulations also compare the proposed estimators with the multiple imputation estimator of Lu and Tsiatis (2001). The application of the proposed method is illustrated using data from a bone marrow transplant study.     

国家综合配套改革试验区的改革与政策法制冲突问题研究

制度因素是区域经济发展的内生变量,政策法律制度是正式制度安排,对区域经济发展具有重要的作用.国家综合配套改革是在政策法律逐步完善基础上的改革,和早期区域经济发展缺少政策法律保障不同,更多的是两者之间的冲突,在行政管理体制领域、经济体制改革领域和社会体制改革领域都有明显表现.解决两者之间的冲突不仅需要国家层面进行解决,也需要试点区域进行推动.     

两类系统的逐点伪轨跟踪性研究

本文主要研究提升系统和逆极限系统,证明了如果基础系统具有逐点伪轨跟踪性,则其提升系统也具有逐点伪轨跟踪性;如果每个fi具有逐点伪轨跟踪性,则诱导映射也具有逐点伪轨跟踪性。     

HP20机器人的运动学逆解计算及模拟仿真

根据Motoman HP20型机器人的结构特点,利用DH方法建立了其运动学方程,并推导出了运动学逆解。将所求得的运动学逆解编写成Matlab程序,计算了末端执行器在正弦曲线轨迹下各个关节角度变化曲线。建立HP20型机器人的多体动力学虚拟样机,将曲线导入驱动虚拟样机,得到模型的运动轨迹。通过对比,目标曲线与运动轨迹吻合良好,验证了运动学逆解及程序的正确性。研究结果为研究在特定工况下,机械臂的运动学、动力学及电机扭矩特性打下了基础。