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统计推断理论和方法及其在生物医学、数据分析与计算等方面的应用
  • 项目名称：统计推断理论和方法及其在生物医学、数据分析与计算等方面的应用
  • 项目类别：面上项目
  • 批准号：11171001
  • 申请代码：A0111
  • 项目来源：国家自然科学基金
  • 研究期限：2012-01-01-2015-12-31
  • 项目负责人：胡舒合
  • 负责人职称：教授
  • 依托单位：安徽大学
  • 批准年度：2011
中文摘要：

我们侧重发展贝叶斯高维数据统计方法及在高维基因组数据分析中的应用。用贝叶斯高维数据统计方法，寻找小N大p数据的精细结构，以贝叶斯观点指导数据挖掘和机器学习，发展有效的统计计算方法；在贝叶斯统计理论及蒙特卡罗计算方法中，积极开拓在高维基因组数据分析中的新领域；力争在简洁条件下，得到混合样本的Bahadur表示的收敛速度和分位数的Berry-Esseen界；研究逆矩问题及其数据分析与计算等结果，研究停时与弱鞅、N-弱鞅的关系，以期获得更多理论和应用成果；研究混合函数型数据的非参数回归函数估计，以期获得估计量的Berry-Esseen界；研究若干相依序列的大数定律、收敛速度等，并应用到较复杂的统计模型中，如非参数回归、半参数回归模型、时间序列等，以期获得相应估计量的相合性、收敛速度、渐近正态性等及其在实际中应用。同时，在具体的科研工作中，对新的问题补充跟进，力争和国内外相关研究同步。

中文主题词： 相依数据；样本分位数；回归模型；弱鞅和N-弱鞅；贝叶斯估计
英文摘要：

Dependent data；Sample quantiles；Regression model；Demimartingales and N-demimartingales；Bayes estimation

英文主题词： Dependent data；Sample quantiles；Regression model；Demimartingales and N-demimartingales；Bayes estimation
结论摘要：

在相依样本和简洁条件下，研究样本分位数估计问题，获得了类似独立样本下的Bahadur表示和Berry-Esseen界。获得了相依数据下的逆矩渐近逼近表达式及其估计量的收敛速度。对弱鞅和N弱鞅的研究过程中，利用停时等技术工具，获得了类似鞅的一些经典结论，如极大值型不等式、Doob型不等式、凹Young 函数型不等式、Marshall型不等式。在统计模型研究过程中，研究相依数据下回归模型非参数估计问题，半参数回归模型中的估计问题，线性模型M估计问题，非线性回归模型参数最小二乘估计问题，获得了有关估计量的渐近结果（如相合性、收敛速度、渐近正态性等）。研究线性回归模型中回归系数和误差方差的经验贝叶斯估计的优良性，并给出相关数据模拟与分析等结果。对生物医学数据进行无进展生存期、生存预测、预测能力等内容研究，取得的成果对许多来自生物医学等领域的数据分析问题提供了有效的解法与理论依据。已发表标注项目号11171001的论文 87 篇，其中81 篇被SCI收录，组织举办2场概率统计学术会议，培养4名博士和14名硕士，项目“相依变量的概率极限理论和统计推断理论”获2014年度安徽省科学技术奖三等奖。在科学研究、学术合作与交流、人才培养等方面取得重要成果，我们胜利地完成了原计划任务。

成果综合统计
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  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
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期刊论文
Predictive power to assist phase 3 go/no go decision based on phase 2 data on a different endpoint
Predicting survival in non-small cell lung cancer by preceding tumor assessment data
常利力下带干扰的双复合Poisson风险过程的生存概率
实时采集中异常值的自动甄别与纠错方法研究
L-1-deficiency of the sample quantile estimator with respect to a kernel quantile estimator
A note on estimation of the mean residual life function with left-truncated and right-censored data
On the strong convergence and some inequalities for negatively superadditive dependent sequences
Complete Convergence for Weighted Sums and Arrays of Rowwise Extended Negatively Dependent Random Va
AANA序列的强大数定律和强收敛速度
A note on complete convergence of weighted sums for array of rowwise AANA random variables
相依函数型数据条件密度估计的渐近性质
Asymptotic Properties of Maximum Quasi-Likelihood Estimates in Generalized Linear Models with "
On Complete Convergence for Weighted Sums of rho*-Mixing Random Variables
On the strong convergence rate for weighted sums of arrays of rowwise negatively orthant dependent r
Strong convergence results for weighted sums of (rho)over-tilde-mixing random variables
Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regress
Strong and Weak Convergence for Asymptotically Almost Negatively Associated Random Variables
Strong Law of Large Numbers of Partial Sums for Pairwise NQD Sequences
The Berry-Esseen bounds for kernel density estimator under dependent sample
Complete convergence and complete moment convergence for a class of random variables
Probability inequalities for END sequence and their applications
Berry-Esseen bound of sample quantiles for phi-mixing random variables
混合序列的Bernstein型不等式及其逆矩
Complete Convergence for Moving Average Process of Martingale Differences
The consistency for estimator of nonparametric regression model based on NOD errors
Some Baum-Katz type results for -mixing random variables with different distributions
Hajek-R,nyi-type inequality and strong law of large numbers for some dependent sequences
Berry-Esseen bound of sample quantiles for negatively associated sequence
Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences
Some exponential inequalities for acceptable random variables and complete convergence
Complete Convergence for Arrays of Rowwise Asymptotically Almost Negatively Associated Random Variab
(α,β)混合序列的强极限定理(英文)
Nonparametric Estimation of Volatility Function with Variable Bandwidth Parameter
Error variance estimation in semi-functional partially linear regression models
Uniform tail asymptotics for the aggregate claims with stochastic discount in the renewal risk model
Complete convergence of weighted sums for arrays of rowwise phi-mixing random variables
Variance Components Testing in ANOVA-Type Mixed Models
On the Rate of Complete Convergence for Weighted Sums of Arrays of Rowwise phi-Mixing Random Variabl
On complete convergence of weighted sums for arrays of rowwise extended negatively dependent random
Complete moment convergence for randomly weighted sums of martingale differences
Complete Consistency of the Estimator of Nonparametric Regression Models Based on (rho)over-tilde-Mi
Complete convergence for weighted sums of arrays of rowwise. (rho)over-tilde-mixing random variables
Some probability inequalities for a class of random variables and their applications
On Strong Convergence for Weighted Sums of a Class of Random Variables
Some inequalities for conditional demimartingales and conditional N-demimartingales
Asymptotic normality of conditional density estimation in the single index model for functional time
Some inequalities for demimartingales and N-demimartingales
Complete convergence for arrays of rowwise negatively orthant dependent random variables
On complete convergence for arrays of rowwise weakly dependent random variables
Attenuation of treatment effect due to measurement variability in assessment of progression-free sur
Extensions of the Borel-Cantelli lemma in general measure spaces
Conditional Density Estimation in the Single Functional Index Model for alpha-Mixing Functional Data
The Berry-Esseen bound of sample quantiles for NA sequence
Complete Convergence and Complete Moment Convergence for Martingale Difference Sequence
On complete convergence for widely orthant-dependent random variables and its applications in nonpar
On Bahadur representation for sample quantiles under alpha-mixing sequence
Nonparametric regression estimation for functional stationary ergodic data with missing at random
Exponential Inequality for (rho)over-tilde-Mixing Sequences and its Applications
Strong convergence for sequences of asymptotically almost negatively associated random variables
线性模型中回归系数和误差方差同时的经验Bayes估计及其优良性
On the Strong Consistency of M-Estimates in Linear Models for Negatively Superadditive Dependent Err
Conditional mean convergence theorems of conditionally dependent random variables under conditions o
Complete moment convergence of pairwise NQD random variables
Some results for demimartingales and N-demimartingales
On the maximal inequalities for conditional demimartingales
The Superiorities of Empirical Bayes Estimation of Variance Components in Random Effects Model
Superiority of empirical Bayes estimation of error variance in linear model
On Complete Convergence of Moving Average Process for AANA Sequence
The Berry-Esseen type bound of sample quantiles for strong mixing sequence
On Complete Convergence of Weighted Sums for Arrays of Rowwise Asymptotically Almost Negatively Asso
ND序列部分和的大偏差和强收敛性
On some maximal inequalities for demimartingales and N-demimartingales based on concave Young functi
NOD随机阵列加权和的完全收敛性
NOD随机阵列的若干强极限定理
φ混合序列的一些收敛性质
（α,β）混合序列的强极限定理（英文）
Strong Laws of Large Numbers for Weighted Sums of Ч-mixing Sequence
两样本相等性的面积统计量检验
Conditional mean convergence theorems of conditionally dependent random variables under conditions of integrability
Convergence Properties for Arrays of Rowwise φ-Mixing Random Variables
Strong Consistency of M Estimator in Linear Model for φ-mixing Samples
自然联系函数下自适应设计广义线性模型的渐近性质
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