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.     

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.     

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.     

On Rates of Convergence for Bayesian Density Estimation

Abstract.  We consider the problem of estimating a compactly supported density taking a Bayesian nonparametric approach. We define a Dirichlet mixture prior that, while selecting piecewise constant densities, has full support on the Hellinger metric space of all commonly dominated probability measures on a known bounded interval. We derive pointwise rates of convergence for the posterior expected density by studying the speed at which the posterior mass accumulates on shrinking Hellinger neighbourhoods of the sampling density. If the data are sampled from a strictly positive, α -Hölderian density, with α  ∈ ( 0,1] , then the optimal convergence rate n^{− α / (2 α +1)} is obtained up to a logarithmic factor. Smoothing histograms by polygons, a continuous piecewise linear estimator is obtained that for twice continuously differentiable, strictly positive densities satisfying boundary conditions attains a rate comparable up to a logarithmic factor to the convergence rate n ^−4/5 for integrated mean squared error of kernel type density estimators.     

Improved Monte Carlo inference for models with additive error

Some statistical models defined in terms of a generating stochastic mechanism have intractable distribution theory, which renders parameter estimation difficult. However, a Monte Carlo estimate of the log-likelihood surface for such a model can be obtained via computation of nonparametric density estimates from simulated realizations of the model. Unfortunately, the bias inherent in density estimation can cause bias in the resulting log-likelihood estimate that alters the location of its maximizer. In this paper a methodology for radically reducing this bias is developed for models with an additive error component. An illustrative example involving a stochastic model of molecular fragmentation and measurement is given.     

网络密度、高管注意力配置与企业绿色创新:制度压力的调节作用

本文整合社会网络理论、注意力基础观和新制度主义理论等,通过对282家制造企业的问卷调查,采用多元回归分析方法,探讨了网络密度和高管注意力配置的交互匹配对企业绿色创新的影响机制,以及制度压力在其中的调节作用。研究发现,在高密度网络中,高管采用注意力聚集策略对绿色创新有显著正向影响;而在低密度网络中,高管采用注意力分散策略对绿色创新有显著正向影响。规制压力和模仿压力均正向调节网络密度和高管注意力配置的交互作用对绿色创新的影响,但模仿压力的调节作用更强。通过构建不同制度压力情景下网络密度与高管注意力的交互作用对绿色创新影响的理论框架,本文推动社会网络理论、注意力基础观等成熟的理论成果从一般创新向绿色创新研究领域繁衍,为企业绿色创新加入与主流理论的对话做了努力,为企业在绿色创新过程中根据不同的制度压力,以及所嵌入的组织间网络密度情况,选择合适的注意力配置策略提供理论参考。