The Sichel model and the mixing and truncation order

The analysis of word frequency count data can be very useful in authorship attribution problems. Zero-truncated generalized inverse Gaussian–Poisson mixture models are very helpful in the analysis of these kinds of data because their model-mixing density estimates can be used as estimates of the density of the word frequencies of the vocabulary. It is found that this model provides excellent fits for the word frequency counts of very long texts, where the truncated inverse Gaussian–Poisson special case fails because it does not allow for the large degree of over-dispersion in the data. The role played by the three parameters of this truncated GIG-Poisson model is also explored. Our second goal is to compare the fit of the truncated GIG-Poisson mixture model with the fit of the model that results from switching the order of the mixing and truncation stages. A heuristic interpretation of the mixing distribution estimates obtained under this alternative GIG-truncated Poisson mixture model is also provided.     

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.     

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.     

脑瘫与正常青少年半蹲起动作的运动学对比分析

运用运动生物力学的录像解析法,对1名正常青少年和4名脑瘫青少年的半蹲起动作进行运动学参数的对比分析,结果显示：在半蹲起动作中,脑瘫I级青少年各参数与正常青少年相比较为接近,脑瘫II级青少年各参数与正常青少年相比差异较大．在完成半蹲起动作中,脑瘫I级青少年双腿用力较为均匀,脑瘫II级青少年以健侧腿发力为主,患侧腿辅助发力来完成动作．     

社会管理创新语境下的死刑问题思考

“社会管理创新”重大命题的提出,为死刑制度改革提供了历史机遇.死刑不仅是一种刑罚方法,更是一种重要的社会管理手段.从符合“善治”目标,避免死刑消极效果,正确看待死刑化解社会矛盾功能等方面的要求出发,在社会管理创新语境中,死刑制度必须进行改革创新.学界应当抓住社会管理创新契机,遵循司法限制到立法减少的路径,积极、渐进推进中国死刑制度改革.     

“四种收入”：破解失地农民可持续生计难题

随着工业化、城镇化进程的不断加快,大量的农用土地被征用,使得失地农民在生活、就业、子女教育、社会保障等方面出现一些问题,因此,把促进失地农民提高增收作为解决问题的重要突破点,分别通过进一步完善后续就业机制、大力发展农村非农产业、健全失地农民＂社会安全网等路径实现失地农民工资性、家庭经营性、财产性、转移性收入保值增值,乃是有效地解决失地农民的可持续生计的关键。