SEMIPARAMETRIC REGRESSION AND GRAPHICAL MODELS

Semiparametric regression models that use spline basis functions with penalization have graphical model representations. This link is more powerful than previously established mixed model representations of semiparametric regression, as a larger class of models can be accommodated. Complications such as missingness and measurement error are more naturally handled within the graphical model architecture. Directed acyclic graphs, also known as Bayesian networks, play a prominent role. Graphical model-based Bayesian 'inference engines', such as bugs and vibes , facilitate fitting and inference. Underlying these are Markov chain Monte Carlo schemes and recent developments in variational approximation theory and methodology.     

当前我国民间信仰问题的现状及对策思考

民间信仰是比较普遍存在的一种特殊而又复杂的文化现象,当前民间信仰领域出现了一些新的问题,民问信仰管理工作也出现了主体不明、管理缺位、法律依据不足等问题。要解决这一问题,一要重视和加强基层政权建设和文化建设：二要对民间信仰的管理模式进行规范和创新;三要加强对民间信仰问题的研究与探索。     

语言的“不可译性”简析

语言的“不可译性”既有“文化不可译性”与“语言不可译性”之分,也有“相对不可译性”与“绝对不可译性”之别,应该具体分析和区别对待。研究语言的“不可译性”,有利于进一步了解不同语言和文化的异同,也有助于进一步探讨翻译理论,尤其是翻译标准。     

“罪名”抑或“具体犯罪行为”之析——对刑法第17条第2款有权解释的几点看法

相对刑事责任年龄的人犯罪,承担刑事责任能力与其年龄密切相关。立法上始终贯彻“以教育为主,惩罚为辅”的方针和“从宽处罚”的原则,对其承担刑事责任的范围作出了及其严格的限制规定。但如何确定犯罪的相对刑事责任年龄人承担刑事责任的范围、触犯的罪名等,在理论上还有待于进一步探讨。     

Forecast mean squared error reductionin the VAR(1) process

When VAR models are used to predict future outcomes, the forecast error can be substantial. Through imposition of restrictions on the off-diagonal elements of the parameter matrix, however, the information in the process may be condensed to the marginal processes. In particular, if the cross-autocorrelations in the system are small and only a small sample is available, then such a restriction may reduce the forecast mean squared error considerably.

In this paper, we propose three different techniques to decide whether to use the restricted or unrestricted model, i.e. the full VAR(1) model or only marginal AR(1) models. In a Monte Carlo simulation study, all three proposed tests have been found to behave quite differently depending on the parameter setting. One of the proposed tests stands out, however, as the preferred one and is shown to outperform other estimators for a wide range of parameter settings.     

Statistical analysis of error for fourth-order ordinary differential equation solvers

We develop an autoregressive integrated moving average (ARIMA) model to study the statistical behavior of the numerical error generated from three fourth-order ordinary differential equation solvers: Milne's method, Adams–Bashforth method and a new method that randomly switches between the Milne and Adams–Bashforth methods. With the actual error data based on three differential equations, we desire to identify an ARIMA model for each data series. Results show that some of the data series can be described by ARIMA models but others cannot. Based on the mathematical form of the numerical error, other statistical models should be investigated in the future. Finally, we assess the multivariate normality of the sample mean error generated by the switching method.     

Generalized Augmentation to Control the False Discovery Exceedance in Multiple Testing

Abstract.  A new multiple testing procedure, the generalized augmentation procedure (GAUGE), is introduced. The procedure is shown to control the false discovery exceedance and to be competitive in terms of power. It is also shown how to apply the idea of GAUGE to achieve control of other error measures. Extensions to dependence are discussed, together with a modification valid under arbitrary dependence. We present an application to an original study on prostate cancer and on a benchmark data set on colon cancer.     

Estimation in capture–recapture models when covariates are subject to measurement errors and missing data

For capture–recapture models when covariates are subject to measurement errors and missing data, a set of estimating equations is constructed to estimate population size and relevant parameters. These estimating equations can be solved by an algorithm similar to the EM algorithm. The proposed method is also applicable to the situation when covariates with no measurement errors have missing data. Simulation studies are used to assess the performance of the proposed estimator. The estimator is also applied to a capture–recapture experiment on the bird species Prinia flaviventris in Hong Kong. The Canadian Journal of Statistics 37: 645–658; 2009 © 2009 Statistical Society of Canada     

Nonparametric density deconvolution by weighted kernel estimators

Nonparametric density estimation in the presence of measurement error is considered. The usual kernel deconvolution estimator seeks to account for the contamination in the data by employing a modified kernel. In this paper a new approach based on a weighted kernel density estimator is proposed. Theoretical motivation is provided by the existence of a weight vector that perfectly counteracts the bias in density estimation without generating an excessive increase in variance. In practice a data driven method of weight selection is required. Our strategy is to minimize the discrepancy between a standard kernel estimate from the contaminated data on the one hand, and the convolution of the weighted deconvolution estimate with the measurement error density on the other hand. We consider a direct implementation of this approach, in which the weights are optimized subject to sum and non-negativity constraints, and a regularized version in which the objective function includes a ridge-type penalty. Numerical tests suggest that the weighted kernel estimation can lead to tangible improvements in performance over the usual kernel deconvolution estimator. Furthermore, weighted kernel estimates are free from the problem of negative estimation in the tails that can occur when using modified kernels. The weighted kernel approach generalizes to the case of multivariate deconvolution density estimation in a very straightforward manner.