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In order to solve the problem of testing multidimensional diffusion models, we develop a test statistic based on Multi-Dimensional Tail Condition Expectations (CTEs). Although it is almost impossible to estimate the transition density matrix of a multidimensional diffusion model directly, the transition density of each component can be estimated and each component can be combined by the CTE to establish a true multidimensional statistics. Finally, the performance of the test is evaluated through simulation.     

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??The paper considers a risk model with two dependent classes of
insurance business. In this model, the two claim number processes are partly sparsely
correlated through an Erlang(2) process. By introducing an auxiliary model, we obtain the
integral equations for ultimate ruin probabilities, and discuss the asymptotic property of
ruin probabilities by renewal approach. We also get the linear differential equations of
ruin probabilities of the model and the corresponding auxiliary model when claims follow
the exponential distributions, and show how solves the linear differential equations by a
specific example.     

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Let, be two independent,
-dimensional sub-fractional Brownian motions with respective indices.
Assume. Our principal results are the necessary and sufficient condition for the
existence and smoothness of the collision local time and the intersection local time of
and through chaos expansion and elementary inequalities.     

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??Recurrent event data usually occur in long-term studies which concern
recurrence rates of the disease. In studies of medical sciences, patients who have infected
with the disease, like cancer, were conventionally regarded as impossible to be cured. However,
with the development of medical sciences, recently those patients were found to be possibly
recovered from the disease. The recurrence rate of the events, which is of primary interest,
may be affected by the cure rate that may exist. Therefore, we proposed semiparametric
statistical analysis for recurrent event data with subjects possibly being cured. In our
approach, we present a proportional rate model for recurrence rate with the cure rate adjusted
through a Logistic regression model, and develop some estimating equations for estimation of
the regression parameters, with their large sample properties, including consistency and
asymptotic normality established. Numerical studies under different settings were conducted
for assessing the proposed methodology and the results suggest that they work well for
practical situations. The approach is applied to a bladder cancer dataset which motivated our
study.     

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本文研究了独立随机变量之和的绝对矩的几个性质, 其中包括$\ep|X+Y|-\ep|X-Y|$的表达式, 这里$X$和$Y$是相互独立的随机变量.     

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多元非参数分位数回归常常是难于估计的, 为了降低维数同时保持非参数估计的灵活性, 人们常常用单指标的方法模拟响应变量的条件分位数. 本文主要研究单指标分位数回归的变量选择. 以最小化平均损失估计为基础, 我们通过最小化具有SCAD惩罚项的平均损失进行变量选择和参数估计. 在正则条件下, 得到了单指标分位数回归SCAD变量选择的Oracle性质, 给出了SCAD变量选择的计算方法, 并通过模拟研究说明了本文所提方法变量选择的样本性质.     

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This paper studies the estimation of change point in mean and variance function of a non-parametric regression model based on kernel estimation and wavelet method. First, kernel estimation of mean function is developed and it is used to estimate the position and jump size of mean change. Second, wavelet methods are applied to derive the variance estimator which is used to estimate the location and jump size of the change point in variance. The asymptotic properties of these estimators are proved. Finally, the results from a numerical simulations and comparison study show that validate the effectiveness of our method.     

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In this paper an efficient estimation methodology for the partially linear models with random effects is proposed. For this, we use the generalized least square estimate (GLSE) and the B-splines methods to estimate the unknowns, and employ the penalized least square method to obtain the estimators of the random effects item. Further, we also consider the estimation for the variance components. Compared with the existing methods, our proposed methodology performs well. The asymptotic properties of the estimators are obtained. A simulation study is carried out to assess the performance of our proposed methodology.     

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This paper assumes that company's asset process follows a non-linear model, which reflects the relationship between the operation costs and the size business. Suppose that the company can control the asset process by changing the size of business, paying dividends and raising money dynamically. Meanwhile, it bears both fixed and proportional transaction costs during the control processes. Under the objective of maximizing the company's value, we obtain the explicit solutions of optimal strategies and value function by using the optimal control method. The results illustrate that the optimal strategies depend on the parameters of the model. The company should expand the business scale with the increasing of asset. Dividends should be paid out according to the impulse control strategy. Financing is profitable to avoid bankruptcy if and only if the transaction costs are relatively low.     

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??How to solve the inference problem of candidate database web surveys is an urgent problem to be solved in the development of web survey. In order to solve this problem, the inference method of non-probability sampling based on superpopulation pseudo design and the combined sample is proposed. A superpopulation model is firstly built up to construct pseudo weights for a survey sample of the web candidate database. The estimator of the population mean is then computed according to the combined sample composed of the survey sample of the web candidate database and a probability sample. The variance estimator of the population mean estimator is lastly derived according to the variance estimation theory of the superpopulation model. The Bootstrap and Jackknife methods are also used to compute the variance estimator. And all these variance estimation methods are compared. The research results show that the population mean estimator based on superpopulation pseudo design and the combined sample is better, and has higher efficiency than the estimator only using the probability sample and the weighted estimator only using the survey sample of the web candidate database. The variance estimator computed by using the VM1, VM2 and VM3 method are relatively better.     

Bayesian Analysis for Random Coefficient Regression Models Using Noninformative Priors

We apply Bayesian approach, through noninformative priors, to analyze a Random Coefficient Regression (RCR) model. The Fisher information matrix, the Jeffreys prior and reference priors are derived for this model. Then, we prove that the corresponding posteriors are proper when the number of full rank design matrices are greater than or equal to twice the number of regression coefficient parameters plus 1 and that the posterior means for all parameters exist if one more additional full rank design matrix is available. A hybrid Markov chain sampling scheme is developed for computing the Bayesian estimators for parameters of interest. A small-scale simulation study is conducted for comparing the performance of different noninformative priors. A real data example is also provided and the data are analyzed by a non-Bayesian method as well as Bayesian methods with noninformative priors.     

多重线性回归模型的贝叶斯预报分析

多重线性回归模型的贝叶斯预报分析是贝叶斯线性模型理论的重要组成部分。通过模型系统的统计结构，证明了矩阵正态-Wishart分布为模型参数的共轭先验分布；利用贝叶斯定理，根据模型的样本似然函数和参数的先验分布推导了参数的后验分布；然后，从数学上严格推断了模型的预报分布密度函数，证明了模型预报分布为矩阵t分布。研究结果表明：由于参数先验分布的作用，样本的预报分布与其原统计分布有着本质性的差异，前服从矩阵正态分布，而后为矩阵t分布。     

模糊线性回归的稳健方法

考虑两类模糊回归模型：一类是设计点为实数,参数为模糊数;另一类是观察值为模糊数、参数为实数。就这两类回归模型,从稳健统计的角度提出相应的稳健方法,并通过例子与现有的方法进行比较,说明所提方法的稳健性。     

带有不可忽略缺失数据的广义部分线性模型的贝叶斯分析

广义部分线性模型是广义线性模型和部分线性模型的推广,是一种应用广泛的半参数模型.本文讨论的是该模型在线性协变量和响应变量均存在非随机缺失数据情形下参数的Bayes估计和基于Bayes因子的模型选择问题,在分析过程中,采用了惩罚样条来估计模型中的非参数成分,并建立了Bayes层次模型;为了解决Gibbs抽样过程中因参数高度相关带来的混合性差以及因维数增加导致出现不稳定性的问题,引入了潜变量做为添加数据并应用了压缩Gibbs抽样方法,改进了收敛性;同时,为了避免计算多重积分,利用了M-H算法估计边缘密度函数后计算Bayes因子,为模型的选择比较提供了一种准则.最后,通过模拟和实例验证了所给方法的有效性.     

Optimal Designs for Balanced Linear Mixed-Effects Regression Models

The paper investigates the problem ofoptimal balanced designs in general linear regression models withmixed effects. The interest lies in estimating fixed effects, randomeffects and prediction of the future observation of an individual,respectively. By using the de la Garaz phenomenon and Loewner orderdomination, the dimension of determining the optimal designs arereduced. The optimal designs are derived by using analytical ornumerical methods, and their optimalities are verified through thegeneral equivalence theorems.     

平衡线性混合效应模型的最优设计

研究了一般平衡线性混合效应模型下的最优设计问题。主要关注模型固定效应估计,随机效应的估计以及对个体未来观察值预测的最优设计。以de la Garaz现象和Loewner偏序为工具降低求解最优设计问题的维度,用解析方法或数值方法求解最优设计,并利用等价性定理判断解的最优性。     

Modified Cross-Validation for Penalized High-Dimensional Linear Regression Models

In this article, for Lasso penalized linear regression models in high-dimensional settings, we propose a modified cross-validation (CV) method for selecting the penalty parameter. The methodology is extended to other penalties, such as Elastic Net. We conduct extensive simulation studies and real data analysis to compare the performance of the modified CV method with other methods. It is shown that the popular K-fold CV method includes many noise variables in the selected model, while the modified CV works well in a wide range of coefficient and correlation settings. Supplementary materials containing the computer code are available online.     

Locally Sparse Estimator for Functional Linear Regression Models

A new locally sparse (i.e., zero on some subregions) estimator for coefficient functions in functional linear regression models is developed based on a novel functional regularization technique called “fSCAD.” The nice shrinkage property of fSCAD allows the proposed estimator to locate null subregions of coefficient functions without over shrinking nonzero values of coefficient functions. Additionally, a roughness penalty is incorporated to control the roughness of the locally sparse estimator. Our method is theoretically sounder and computationally simpler than existing methods. Asymptotic analysis reveals that the proposed estimator is consistent and can identify null subregions with probability tending to one. Extensive simulations confirm the theoretical analysis and show excellent numerical performance of the proposed method. Practical merit of locally sparse modeling is demonstrated by two real applications. Supplemental materials for the article are available online.     

泊松逆高斯回归模型的贝叶斯统计推断

本文研究泊松逆高斯回归模型的贝叶斯统计推断.基于应用Gibbs抽样,Metropolis-Hastings算法以及Multiple-Try Metropolis算法等MCMC统计方法计算模型未知参数和潜变量的联合贝叶斯估计,并引入两个拟合优度统计量来评价提出的泊松逆高斯回归模型的合理性.若干模拟研究与一个实证分析说明方...     

线性回归模型的Bayes统计推断

Bayes方法虽融合了样本信息和先验信息，但利用的先验信息都是有历史经验和专家估计所得，因此可靠度不高。该文研究了正态线性回归模型：Y=Xβ＋e，e—N（0，σ^2。L），其中σ^2已知，β为未知参数向量，对传统的Bayes方法进行了改进，即把Bayes方法中的后验信息作为改进Bayes的无验信息并融合样本信息进行统计推断，在二次损失函数下得到了β的改进的Bayes估计。由于改进的Bayes方法的先验信息中有样本信息，因此其准确度比传统的Bayes方法准确度更高。