Deconvolution with supersmooth distributions

Nonparametric deconvolution problems require one to recover an unknown density when the data are contaminated with errors. Optimal global rates of convergence are found under the weighted L_p-loss (1 ≤ p ≤ ∞). It appears that the optimal rates of convergence are extremely low for supersmooth error distributions. To resolve this difficulty, we examine how high the noise level can be for deconvolution to be feasible, and for the deconvolution estimate to be as good as the ordinary density estimate. It is shown that if the noise level is not too high, nonparametric Gaussian deconvolution can still be practical. Several simulation studies are also presented.     

分析Chiral分层媒质特性的一般方法(英文)

提出了一套系统方法用于求解任意导体片位于界面的Chiral分层媒质的谐振频率,衰减因子和电磁场分布。文中的分析是在Fourier变换域的并矢格林函数和矩阵分析的基础上来进行的,给出的公式的最大价值在于它提供了求解Chiral分层媒质问题的方法论。     

Modified cross-validation in density estimation

We propose a new modified (biased) cross-validation method for adaptively determining the bandwidth in a nonparametric density estimation setup. It is shown that the method provides consistent minimizers. Some simulation results are reported on which compare the small sample behavior of the new and the classical cross-validation selectors.     

密度分布非均匀的反馈控制Logistic单种群模型平衡态的稳定性

本文对种群密度在非均匀分布情形下,考虑了具反馈控制的滞后 Logistic 生态模型平衡位置的稳定性;分别给出了在常时滞和弱连续时滞以及强连续时滞情况下的稳定性条件;其结果是对 Gopalsamy 在密度均匀分布情形下相应结果的推广.     

Semi-parametric estimation of ROC curves based on binomial regression modelling

This paper presents a method of estimating a receiver operating characteristic (ROC) curve when the underlying diagnostic variable X is continuous and fully observed. The new method is based on modelling the probability of response given X , rather than the distribution of X given response. The method offers advantages in modelling flexibility and computational simplicity. The resulting ROC curve estimates are semi-parametric and can, in principle, take an infinite variety of shapes. Moreover, model selection can be based on standard methods within the binomial regression framework. Statistical accuracy of the curve estimate is provided by a simply implemented bootstrap approach.     

一类边值问题临界解的扰动性质

在LP(1 p <+∞ ) 空间中证明了一类非齐次积一秩微分方程边值问题的临界解关于方程系数和区域尺寸的连续依赖性 ,并获得了相应的高阶扰动公式     

Nyquist采样频率下的频谱失真与采样定理

本文通过在Nyquist采样率下对信号的频谱是否发生失真，发生了怎样的失真的讨论，分析了在进行离散傅立叶变换（DFT）时，采样定理在其边界条件下进行信号处理时存在的问题。展示了在该条件下频谱发生严重失真的形式和程度，最后从无失真地恢复时域信号x(t）的角度讨论了DFT意义下采样定理的表述。     

On the asymptotic normality of the L1- and L2-errors in histogram density estimation

The L₁ and L₂-errors of the histogram estimate of a density f from a sample X₁,X₂,…,Xn using a cubic partition are shown to be asymptotically normal without any unnecessary conditions imposed on the density f. The asymptotic variances are shown to depend on f only through the corresponding norm of f. From this follows the asymptotic null distribution of a goodness-of-fit test based on the total variation distance, introduced by Györfi and van der Meulen (1991). This note uses the idea of partial inversion for obtaining characteristic functions of conditional distributions, which goes back at least to Bartlett (1938).     

近代河南集市研究再思考

近代集市的发展不仅表现为数量方面的增加,也有集市数量不变而集市承载量增加的情况;考察集市分布密度以耕地面积为基础更有可比性,而且开市率的高低主要是人们传统习惯、人口规模、集市密度、商品化程度、经济发展状况等因素综合作用的结果,其中传统习惯对开市率的影响较大。     

Data skeletons: simultaneous estimation of multiple quantiles for massive streaming datasets with applications to density estimation

We consider the problem of density estimation when the data is in the form of a continuous stream with no fixed length. In this setting, implementations of the usual methods of density estimation such as kernel density estimation are problematic. We propose a method of density estimation for massive datasets that is based upon taking the derivative of a smooth curve that has been fit through a set of quantile estimates. To achieve this, a low-storage, single-pass, sequential method is proposed for simultaneous estimation of multiple quantiles for massive datasets that form the basis of this method of density estimation. For comparison, we also consider a sequential kernel density estimator. The proposed methods are shown through simulation study to perform well and to have several distinct advantages over existing methods.