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We establish a quenched central limit theorem (CLT) for the branching Brownian motion with random immigration in dimension $d\geq4$. The limit is a Gaussian random measure, which is the same as the annealed central limit theorem, but the covariance kernel of the limit is different from that in the annealed sense when d=4.     

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In this paper, we study the stochastic comparisons of order statistics from generalized normal distributions. We obtain some sufficient conditions for ordering results based on parameter matrix and vector majorization comparisons. These conditions are necessary in some cases.     

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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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In this paper, we consider the estimation problemfor partially linear models with additive measurement errors in thenonparametric part. Two kinds of estimators are proposed. The first oneis an integral moment-based estimator with deconvolution kernel techniques,associated with the strong consistency for the estimator. Another oneis a simulation-based estimator to avoid the integrals involved in theintegral moment-based estimator. Simulation studies are conducted toexamine the performance of the proposed estimators.     

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Take any subcritical offspring distribution with bounded support and consider the corresponding Galton--Watson tree. In this short note we condition this Galton--Watson tree on large width and show that the conditioned tree does not converge locally to any random tree with at most one infinite spine.     

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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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Reference分析最早由Bernardo(1979)提出的, Berger和Bernardo(1992a)做了进一步的发展. 而Berger 等(2001)提出了一个获得精确reference先验的方法, 它已经成为获取无信息先验的最成功的方法之一. 本文基于Berger等(2001)所提出的的算法, 研究了具有一般协方差结构的增长曲线模型的reference先验. 同时, 给出了相应结果的一些应用.     

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??This paper develops a covariate-adjusted precision matrix estimation using a two-stage estimation procedure. Firstly, we identify the relevant covariates that affect the means by a joint l_1 penalization. Then, the estimated regression coefficients are used to estimate the mean values in a multivariate sub-Gaussian model in order to estimate the sparse precision matrix through a Lasso penalized D-trace loss. Under some assumptions, we establish the convergence rate of the precision matrix estimation under different norms and demonstrate the sparse recovery property with probability converging to one. Simulation shows that our methods have the finite-sample performance compared with other methods.     

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首先, 当$Q$是一个拟单调的q矩阵的时候,我们找出最小的$Q$函数是一个Feller的转移函数的准则.然后我们把这个结论应用于生成分支q矩阵并得到相应的生成分支过程的Feller准则.特别地, 设$theta$是分支q矩阵中的非线性数,总是存在一个分点$theta_0$满足$1leqtheta_0leq2$或$theta_0<+infty$使得生成分支过程是否是Feller的要依据$thetatheta_0$.     

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本文将辅助--充分交织策略, 即Yu和Meng (2011)中提到的ASIS算法, 应用于Gibbs抽样算法中以提高两个方差参数的收敛性. 我们通过对潜在规模缩减因子(PSRF)、轨迹图及后验估计 比较了ASIS算法与普通Gibbs抽样算法的性能, 其中一个参数的收敛性有了很大的提高, 但另一个参数没有很明显的提高. 然而, 由于ASIS算法相与普通的Gibbs抽样算法相比极大地减少了为达到收敛所 需要的循环次数, 整体的抽样性能得到了极大的提高.