Local influence in multilevel models

The authors study the local influence of observations in multilevel regression models. To this end, they perturb simultaneously the variances, responses and design matrix. To measure the local change caused by these perturbations, they use generalized Cook statistics for the fixed and random parameter estimates. Closed form local influence measures also allow them to assess the joint influence of various observations. They suggest a simple computation method and illustrate their results using two examples.     

A theoretical basis for perturbation methods

In this paper we discuss a new theoretical basis for perturbation methods. In developing this new theoretical basis, we define the ideal measures of data utility and disclosure risk. Maximum data utility is achieved when the statistical characteristics of the perturbed data are the same as that of the original data. Disclosure risk is minimized if providing users with microdata access does not result in any additional information. We show that when the perturbed values of the confidential variables are generated as independent realizations from the distribution of the confidential variables conditioned on the non-confidential variables, they satisfy the data utility and disclosure risk requirements. We also discuss the relationship between the theoretical basis and some commonly used methods for generating perturbed values of confidential numerical variables.     

随机型细胞神经网络的稳定性

借助于李雅谱洛夫理论、矩阵分析方法和It?公式,结合不等式分析技巧,研究了随机细胞神经网络系统的均方指数稳定性,给出了系统的解的二阶矩Liapunov指数估计式和均方指数稳定的充分条件。     

Generalized Leverage and its Applications

The generalized leverage of an estimator is defined in regression models as a measure of the importance of individual observations. We derive a simple but powerful result, developing an explicit expression for leverage in a general M -estimation problem, of which the maximum likelihood problems are special cases. A variety of applications are considered, most notably to the exponential family non-linear models. The relationship between leverage and local influence is also discussed. Numerical examples are given to illustrate our results     

Bayesian bridge-randomized penalized quantile regression estimation for linear regression model with AP(q) perturbation

Bridge penalized regression has many desirable statistical properties such as unbiasedness, sparseness as well as ‘oracle’. In Bayesian framework, bridge regularized penalty can be implemented based on generalized Gaussian distribution (GGD) prior. In this paper, we incorporate Bayesian bridge-randomized penalty and its adaptive version into the quantile regression (QR) models with autoregressive perturbations to conduct Bayesian penalization estimation. Employing the working likelihood of the asymmetric Laplace distribution (ALD) perturbations, the Bayesian joint hierarchical models are established. Based on the mixture representations of the ALD and generalized Gaussian distribution (GGD) priors of coefficients, the hybrid algorithms based on Gibbs sampler and Metropolis-Hasting sampler are provided to conduct fully Bayesian posterior estimation. Finally, the proposed Bayesian procedures are illustrated by some simulation examples and applied to a real data application of the electricity consumption.     

Conditional Akaike Information Criteria for a Class of Poisson Mixture Models with Random Effects

Focusing on the model selection problems in the family of Poisson mixture models (including the Poisson mixture regression model with random effects and zero‐inflated Poisson regression model with random effects), the current paper derives two conditional Akaike information criteria. The criteria are the unbiased estimators of the conditional Akaike information based on the conditional log‐likelihood and the conditional Akaike information based on the joint log‐likelihood, respectively. The derivation is free from the specific parametric assumptions about the conditional mean of the true data‐generating model and applies to different types of estimation methods. Additionally, the derivation is not based on the asymptotic argument. Simulations show that the proposed criteria have promising estimation accuracy. In addition, it is found that the criterion based on the conditional log‐likelihood demonstrates good model selection performance under different scenarios. Two sets of real data are used to illustrate the proposed method.     

Information preserving statistical obfuscation

The problem of limiting the disclosure of information gathered on a set of companies or individuals (the respondents) is considered, the aim being to provide useful information while preserving confidentiality of sensitive information. The paper proposes a method which explicitly preserves certain information contained in the data. The data are assumed to consist of two sets of information on each respondent: public data and specific survey data. It is assumed in this paper that both sets of data are liable to be released for a subset of respondents. However, the public data will be altered in some way to preserve confidentiality whereas the specific survey data is to be disclosed without alteration. The paper proposes a model based approach to this problem by utilizing the information contained in the sufficient statistics obtained from fitting a model to the public data by conditioning on the survey data. Deterministic and stochastic variants of the method are considered.     

一类非线性奇摄动方程的周期

探讨了方程εy' f(t,y,y')y=0的周期性,给出了周期解存在的一些条件,并进行了实例分析.     

静电电子回旋脉塞的单粒子理论

本文用单粒子理论研究了静电电子回旋脉塞。通过对静电电子回旋脉塞中的电子运动的分析,导出了电子与波互作用的非线性摆方程。文中用二阶扰动方法求解非线性摆方程,得到了TE_(mn)和TM_(mn)两种工作模式的静电电子回旋脉塞不稳定性线性增益公式,进一步证实了静电电子回旋脉塞不稳定性是存在的。