Evaluating the Use of Spatial Covariance Structures in the Analysis of Cardiovascular Imaging Data

This article investigates the choice of working covariance structures in the analysis of spatially correlated observations motivated by cardiac imaging data. Through Monte Carlo simulations, we found that the choice of covariance structure affects the efficiency of the estimator and power of the test. Choosing the popular unstructured working covariance structure results in an over-inflated Type I error possibly due to a sample size not large enough relative to the number of parameters being estimated. With regard to model fit indices, Bayesian Information Criterion outperforms Akaike Information Criterion in choosing the correct covariance structure used to generate data.     

A Necessary Condition for the Strong Oracle Property

A problem of using a non‐convex penalty for sparse regression is that there are multiple local minima of the penalized sum of squared residuals, and it is not known which one is a good estimator. The aim of this paper is to give a guide to design a non‐convex penalty that has the strong oracle property. Here, the strong oracle property means that the oracle estimator is the unique local minimum of the objective function. We summarize three definitions of the oracle property – the global, weak and strong oracle properties. Then, we give sufficient conditions for the weak oracle property, which means that the oracle estimator becomes a local minimum. We give an example of non‐convex penalties that possess the weak oracle property but not the strong oracle property. Finally, we give a necessary condition for the strong oracle property.     

A Seemingly Unrelated Nonparametric Additive Model with Autoregressive Errors

This article considers a nonparametric additive seemingly unrelated regression model with autoregressive errors, and develops estimation and inference procedures for this model. Our proposed method first estimates the unknown functions by combining polynomial spline series approximations with least squares, and then uses the fitted residuals together with the smoothly clipped absolute deviation (SCAD) penalty to identify the error structure and estimate the unknown autoregressive coefficients. Based on the polynomial spline series estimator and the fitted error structure, a two-stage local polynomial improved estimator for the unknown functions of the mean is further developed. Our procedure applies a prewhitening transformation of the dependent variable, and also takes into account the contemporaneous correlations across equations. We show that the resulting estimator possesses an oracle property, and is asymptotically more efficient than estimators that neglect the autocorrelation and/or contemporaneous correlations of errors. We investigate the small sample properties of the proposed procedure in a simulation study.     

Variable selection in additive quantile regression using nonconcave penalty

This paper considers variable selection in additive quantile regression based on group smoothly clipped absolute deviation (gSCAD) penalty. Although shrinkage variable selection in additive models with least-squares loss has been well studied, quantile regression is sufficiently different from mean regression to deserve a separate treatment. It is shown that the gSCAD estimator can correctly identify the significant components and at the same time maintain the usual convergence rates in estimation. Simulation studies are used to illustrate our method.     

略论中国古代法律的基本性质——兼谈中国古代无民法

关于中国古代法律,"诸法合体,民刑不分"的习惯说法并不妥当,它意味着诸法都有,没有分开而已;民法之说则似是而非,模糊了民法与刑法的区别,也模糊了古今与中西法律的基本区别.在中国古代特定的社会历史条件下,法律作为维护家天下统治秩序的工具,核心是一个"刑"字,是泛化的刑罚.它无所谓民事与刑事的区分,只有事之大小、刑之轻重,故与民法无关,也不等同于刑法,勉强可视为一种片面的刑法.实际上,中国古代社会无从产生民法,民间社会关系与纠纷概由律及礼、俗调节.     

Multivariate process dispersion monitoring without subgrouping

The memory-type adaptive and non-adaptive control charts are among the best control charts for detecting small-to-moderate changes in the process parameter(s). In this paper, we propose the Crosier CUSUM (CCUSUM), EWMA, adaptive CCUSUM (ACCUSUM) and adaptive EWMA (AEWMA) charts for efficiently monitoring the changes in the covariance matrix of a multivariate normal process without subgrouping. Using extensive Monte Carlo simulations, the length characteristics of these control charts are computed. It turns out that the ACCUSUM and AEWMA charts perform uniformly and substantially better than the CCUSUM and EWMA charts when detecting a range of shift sizes in the covariance matrix. Moreover, the AEWMA chart outperforms the ACCUSUM chart. A real dataset is used to explain the implementation of the proposed control charts.     

Designing and integrating composite networks for monitoring multivariate gaussian pollution fields

Networks of ambient monitoring stations are used to monitor environmental pollution fields such as those for acid rain and air pollution. Such stations provide regular measurements of pollutant concentrations. The networks are established for a variety of purposes at various times so often several stations measuring different subsets of pollutant concentrations can be found in compact geographical regions. The problem of statistically combining these disparate information sources into a single 'network' then arises. Capitalizing on the efficiencies so achieved can then lead to the secondary problem of extending this network. The subject of this paper is a set of 31 air pollution monitoring stations in southern Ontario. Each of these regularly measures a particular subset of ionic sulphate, sulphite, nitrite and ozone. However, this subset varies from station to station. For example only two stations measure all four. Some measure just one. We describe a Bayesian framework for integrating the measurements of these stations to yield a spatial predictive distribution for unmonitored sites and unmeasured concentrations at existing stations. Furthermore we show how this network can be extended by using an entropy maximization criterion. The methods assume that the multivariate response field being measured has a joint Gaussian distribution conditional on its mean and covariance function. A conjugate prior is used for these parameters, some of its hyperparameters being fitted empirically.     

Standard errors for EM estimation

The EM algorithm is a popular method for computing maximum likelihood estimates. One of its drawbacks is that it does not produce standard errors as a by-product. We consider obtaining standard errors by numerical differentiation. Two approaches are considered. The first differentiates the Fisher score vector to yield the Hessian of the log-likelihood. The second differentiates the EM operator and uses an identity that relates its derivative to the Hessian of the log-likelihood. The well-known SEM algorithm uses the second approach. We consider three additional algorithms: one that uses the first approach and two that use the second. We evaluate the complexity and precision of these three and the SEM in algorithm seven examples. The first is a single-parameter example used to give insight. The others are three examples in each of two areas of EM application: Poisson mixture models and the estimation of covariance from incomplete data. The examples show that there are algorithms that are much simpler and more accurate than the SEM algorithm. Hopefully their simplicity will increase the availability of standard error estimates in EM applications. It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation. Some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.     

The covariance of the backward and forward recurrence times in a renewal process: the stationary case and asymptotics for the ordinary case

In a Poisson process, it is well-known that the forward and backward recurrence times at a given time point t are independent random variables. In a renewal process, although the joint distribution of these quantities is known (asymptotically), it seems that very few results regarding their covariance function exist. In the present paper, we study this covariance and, in particular, we state both necessary and sufficient conditions for it to be positive, zero or negative in terms of reliability classifications and the coefficient of variation of the underlying inter-renewal and the associated equilibrium distribution. Our results apply either for an ordinary renewal process in the steady state or for a stationary process.     

民俗控制与祥林嫂之死——对《祝福》的另一种解读方式

关于《祝福》中祥林嫂之死因,是个老而又老的话题。作为鲁迅最著名的乡土题材小说,《祝福》蕴涵着丰富的民俗文化,本文从民俗传统对俗民个体的控制与教化角度,认为隐喻型民俗控制和奖惩型民俗控制是造成祥林嫂之死的最主要的主客观原因。鲁迅以此深刻揭示了封建文化思想吃人的本质。