部分区间删失数据既包含精确数据也包含区间删失数据，这类数据常见于生物与医学研究中.对于右删失数据的统计推断问题，已有大量文献问世，而对于既包含精确值和区间删失的数据，相关研究较为罕见.Huang将部分区间删失数据分为第一类部分区间删失数据与第二类部分区间删失数据，本文考虑第一类部分区间删失数据下Weibull分布中未知参数最大似然估计的渐近性质.在一定的正则性条件下证明了最大似然估计的强相合性以及渐近正态性.模拟结果显示相合性及渐近正态性的结论是合理的.

We present a novel nonparametric approach for estimating average treatment effects (ATEs), addressing a fundamental challenge in causal inference research, both in theory and empirical studies. Our method offers an effective solution to mitigate the instability problem caused by propensity scores close to zero or one, which are commonly encountered in (augmented) inverse probability weighting approaches. Notably, our method is straightforward to implement and does not depend on outcome model specification. We introduce an estimator for ATE and establish its consistency and asymptotic normality through rigorous analysis. To demonstrate the robustness of our method against extreme propensity scores, we conduct an extensive simulation study. Additionally, we apply our proposed methods to estimate the impact of social activity disengagement on cognitive ability using a nationally representative cohort study. Furthermore, we extend our proposed method to estimate the ATE on the treated population.

证明了残差平方和增量与残差平方和的独立性、拟合值向量与学生化残差的独立性,并给出判断两个向量独立性的一个充分性条件.

This article discusses regression analysis of mixed interval-censored failure time data. Such data frequently occur across a variety of settings, including clinical trials, epidemiologic investigations, and many other biomedical studies with a follow-up component. For example, mixed failure times are commonly found in the two largest studies of long-term survivorship after childhood cancer, the datasets that motivated this work. However, most existing methods for failure time data consider only right-censored or only interval-censored failure times, not the more general case where times may be mixed. Additionally, among regression models developed for mixed interval-censored failure times, the proportional hazards formulation is generally assumed. It is well-known that the proportional hazards model may be inappropriate in certain situations, and alternatives are needed to analyze mixed failure time data in such cases. To fill this need, we develop a maximum likelihood estimation procedure for the proportional odds regression model with mixed interval-censored data. We show that the resulting estimators are consistent and asymptotically Gaussian. An extensive simulation study is performed to assess the finite-sample properties of the method, and this investigation indicates that the proposed method works well for many practical situations. We then apply our approach to examine the impact of age at cranial radiation therapy on risk of growth hormone deficiency in long-term survivors of childhood cancer.

Partly interval censored data frequently occur in many areas including clinical trials, epidemiology research, and medical follow-up studies. When data come from observational studies, we need to carefully adjust for the confounding bias in order to estimate the true treatment effect. Pair matching designs are popular for removing confounding bias without parametric assumptions. With time-to-event outcomes, there are some literature for hypothesis testing with paired right censored data, but not for interval censored data. O'Brien and Fleming extended the Prentice Wilcoxon test to right censored paired data by making use of the PrenticeWilcoxon scores. Akritas proposed the Akritas test and established its asymptotic properties. We extend Akritas test to partly interval censored data. We estimate the survival distribution function by nonparametric maximum likelihood estimation (NPMLE), and prove the asymptotic validity of the new test. To improve our test under small sample size or extreme distributions, we also propose a modified version using the rank of the score difference. Simulation results indicate that our proposed methods have very good performance.

This paper discusses the transformed linear regression with non-normal error distributions, a problem that often occurs in many areas such as economics and social sciences as well as medical studies. The linear transformation model is an important tool in survival analysis partly due to its flexibility. In particular, it includes the Cox model and the proportional odds model as special cases when the error follows the extreme value distribution and the logistic distribution, respectively. Despite the popularity and generality of linear transformation models, however, there is no general theory on the maximum likelihood estimation of the regression parameter and the transformation function. One main difficulty for this is that the transformation function near the tails diverges to infinity and can be quite unstable. It affects the accuracy of the estimation of the transformation function and regression parameters. In this paper, we develop the maximum likelihood estimation approach and provide the near optimal conditions on the error distribution under which the consistency and asymptotic normality of the resulting estimators can be established. Extensive numerical studies suggest that the methodology works well, and an application to the data on a typhoon forecast is provided.

Time-to-event data are very common in observational studies. Unlike randomized experiments, observational studies suffer from both observed and unobserved confounding biases. To adjust for observed confounding in survival analysis, the commonly used methods are the Cox proportional hazards (PH) model, the weighted logrank test, and the inverse probability of treatment weighted Cox PH model. These methods do not rely on fully parametric models, but their practical performances are highly influenced by the validity of the PH assumption. Also, there are few methods addressing the hidden bias in causal survival analysis. We propose a strategy to test for survival function differences based on the matching design and explore sensitivity of the P-values to assumptions about unmeasured confounding. Specifically, we apply the paired Prentice-Wilcoxon (PPW) test or the modified PPW test to the propensity score matched data. Simulation studies show that the PPW-type test has higher power in situations when the PH assumption fails. For potential hidden bias, we develop a sensitivity analysis based on the matched pairs to assess the robustness of our finding, following Rosenbaum's idea for nonsurvival data. For a real data illustration, we apply our method to an observational cohort of chronic liver disease patients from a Mayo Clinic study. The PPW test based on observed data initially shows evidence of a significant treatment effect. But this finding is not robust, as the sensitivity analysis reveals that the P-value becomes nonsignificant if there exists an unmeasured confounder with a small impact.

Since the publication of the seminal paper by Cox (1972), proportional hazard model has become very popular in regression analysis for right censored data. In observational studies, treatment assignment may depend on observed covariates. If these confounding variables are not accounted for properly, the inference based on the Cox proportional hazard model may perform poorly. As shown in Rosenbaum and Rubin (1983), under the strongly ignorable treatment assignment assumption, conditioning on the propensity score yields valid causal effect estimates. Therefore we incorporate the propensity score into the Cox model for causal inference with survival data. We derive the asymptotic property of the maximum partial likelihood estimator when the model is correctly specified. Simulation results show that our method performs quite well for observational data. The approach is applied to a real dataset on the time of readmission of trauma patients. We also derive the asymptotic property of the maximum partial likelihood estimator with a robust variance estimator, when the model is incorrectly specified.

部分区间删失数据包括精确数据以及区间删失数据,在慢性病研究中有广泛的应用.本文主要考虑在具有1类部分删失数据下指数分布中最大似然估计的相合性,在一定的正则条件下证明了最大似然估计的强相合性.

Partly interval censored data consist of exact data and interval censored data and arise frequently in the study of chronic diseases.This paper mainly considers the limit properties of MLE for exponential model with partly interval censored data and proves the consistency and asymptotic normality of the MLE for the exponential model with case 2partly interval censored data under some regular conditions.

To compare multiple outcomes between groups in biomedical research,parametric procedure such as multivariate ANOVA or the Bonferroni procedure are used,with the assumption of multivariate normality.Since the assumption of multivariate normality may be false,nonparametric procedures robust against distributions such as MAX test and SAR,are advised naturally.In this article,we provide a new robust test.

Based on the definition approach of two-parameter Markov process,single-parameter strong Markov process and the relationship between the various stopping points,the 1-strong Markov process,the 2-strong Markov process and the wide-future strong Markov process with non-random parameter transformation were defined.Under the condition of random process being progressive measurability,the *-strong Markov process must be a 1,2-strong Markov process,the 1,2-strong Markov process must be a single-point strong Markov process.Under the condition of (F 4 ),the 1,2-strong Markov process must be a single-point strong Markov process.Wide-future strong Markov process must be a single-point strong Markov process.

We consider Exponential transform and Logarithmic transform when the linear regression model is failed.We get the principle of determining unknown parameter and use SPSS to solve it.In the end,we get the analytic formula and some properties of Hat matrix.

From Buffon's Problem,by using the formula calculation of the probability of segment intersecting parallel lines,we get the probability of convex polygon intersecting parallel lines,and then by using approximation theorem,we can get the probability of convex figure intersecting parallel lines,and finally,we point out that the probability of general figure intersecting parallel lines is the same as the probability of its convex hull intersecting parallel lines.

This paper attempts to explain some key concepts deeply in probability theory,aimed to make readers have a further understanding of the concepts such as randomevent,random variable and probability density function.It also proves the formula of solving probability density function and the probability density transformation formula under weaker condition.

This paper gives the theory of Permutation Test,and uses it to solve a statistical problem in medicine.The result shows that the d-ANC(ord-PLT)of the two groups .In adition,when the sample data is large enough,we can use Two Sample t Test.

分析了运筹学课程的特色和教学中存在的问题。针对存在的问题,从优化教学内容、改善教学方法、改进教学手段、开辟第二课堂、建立多元化的考核体系等方面进行了探讨,提出了运筹学课程的教改思路。