Random sliced inverse regression

Sliced Inverse Regression (SIR; 1991) is a dimension reduction method for reducing the dimension of the predictors without losing regression information. The implementation of SIR requires inverting the covariance matrix of the predictors—which has hindered its use to analyze high-dimensional data where the number of predictors exceed the sample size. We propose random sliced inverse regression (rSIR) by applying SIR to many bootstrap samples, each using a subset of randomly selected candidate predictors. The final rSIR estimate is obtained by aggregating these estimates. A simple variable selection procedure is also proposed using these bootstrap estimates. The performance of the proposed estimates is studied via extensive simulation. Application to a dataset concerning myocardial perfusion diagnosis from cardiac Single Proton Emission Computed Tomography (SPECT) images is presented.     

Dimension reduction for the conditional mean and variance functions in time series

This paper deals with the nonparametric estimation of the mean and variance functions of univariate time series data. We propose a nonparametric dimension reduction technique for both mean and variance functions of time series. This method does not require any model specification and instead we seek directions in both the mean and variance functions such that the conditional distribution of the current observation given the vector of past observations is the same as that of the current observation given a few linear combinations of the past observations without loss of inferential information. The directions of the mean and variance functions are estimated by maximizing the Kullback–Leibler distance function. The consistency of the proposed estimators is established. A computational procedure is introduced to detect lags of the conditional mean and variance functions in practice. Numerical examples and simulation studies are performed to illustrate and evaluate the performance of the proposed estimators.     

关于线性变换的根子空间

本文系统论述了属于线性变换特征概念范围的根子空间的基本问题，主要的有两点：（１）根向量所属于的特征值的唯一性；（２）根子空间与特征子空间的结构关系，作为论述这两个问题的预备定理，文中还证明了根向量或根子空间的其它两个重要性质。     

麦克风阵列二维方向估计聚焦算法研究

聚焦算法是解决宽带信号方向(DOA)估计问题的重要算法。常规的宽带聚焦算法需要进行预估计和多次迭代,算法的计算复杂度较高。该文根据宽带聚焦算法的思想,结合语音信号的特点,以各频率点的频域相关矩阵和聚焦点的相关矩阵的均方误差最小为最优化准则,提出了一种不需要预估计和迭代的二维宽带聚焦算法。该算法实时性好、计算复杂度低。采用八元均匀圆环麦克风阵列,仿真验证了该算法的良好二维DOA估计性能。     

一致有界实值函数集上的最佳同时逼近

给出了最佳同时逼近的特征定理 ,并由此导出了最佳同时逼近的交错定理和强唯一性定理     

Trace pursuit variable selection for multi-population data

Variable selection is a very important tool when dealing with high dimensional data. However, most popular variable selection methods are model based, which might provide misleading results when the model assumption is not satisfied. Sufficient dimension reduction provides a general framework for model-free variable selection methods. In this paper, we propose a model-free variable selection method via sufficient dimension reduction, which incorporates the grouping information into the selection procedure for multi-population data. Theoretical properties of our selection methods are also discussed. Simulation studies suggest that our method greatly outperforms those ignoring the grouping information.     

通用教学技术构成论--视点结构教学技术系统建构研究

视点结构教学技术系统是我们历时十余年、经多项有关课题的持续探索研究,建构的一整套具有普适性的科学有效的教学行为方式.作为通用教学技术,其相互联系的三个构成方面从不同侧面相互补充,在操作性的技术层面共同揭示了教学活动整体系统的各层面教学因素及其内在有机联系,从而成为教学常式.视点结构教学基本模式揭示了教学运行过程的基本逻辑环节及程序,视点结构教学要素结构揭示了教学基本因素及其内在相互关系,视点结构教学行为体系则呈现并揭示了教学科学基本原理决定的教学基本模式及教学要素结构落实到实际课堂上而形成的科学有效教学的行为规程及要领系统.     

简并能级的三阶微扰修正

讨论了简并能级的三阶微扰修正问题,给出了一阶修正和二阶修正简并部分解除情况下的三阶能量修正,也讨论了一阶修正简并未完全解除时的三阶能量修正.     

关于n维射影空间的配极对应的一点注记

本文论述了 n 维射影空间中线性子空间关于二阶超曲面配极对应的性质,提出了构造自极超n 1面体的具体方法,从而可把非退化二阶超曲面方程化为标准形式.     

关于模糊向量组的线性关系及模糊子空间的性质

本文在[l]的基础上给出了一个模糊向量组线性相关的充要条件及几个推论,且以定理的形式给出了模糊子空间的若干性质。