具有变系数的2n阶中立型微分方程正解的存在性

本文给出具有变系数Ｐ（ｔ）的２ｎ阶中立型微分方程 （ｘ（ｔ）－Ｐ（ｔ）_ｘ（ｔ－τ））~（２ｎ）+ｆ（ｔ,ｘ（ｔ－τ_1（ｔ））,...,ｘ（ｔ－τ_ｍ（ｔ）））＝０正解存在的若干个充分条件．本文结果部分地回答了文［１］提出的问题．     

Investigation about a screening step in model selection

In many studies a large number of variables is measured and the identification of relevant variables influencing an outcome is an important task. For variable selection several procedures are available. However, focusing on one model only neglects that there usually exist other equally appropriate models. Bayesian or frequentist model averaging approaches have been proposed to improve the development of a predictor. With a larger number of variables (say more than ten variables) the resulting class of models can be very large. For Bayesian model averaging Occam’s window is a popular approach to reduce the model space. As this approach may not eliminate any variables, a variable screening step was proposed for a frequentist model averaging procedure. Based on the results of selected models in bootstrap samples, variables are eliminated before deriving a model averaging predictor. As a simple alternative screening procedure backward elimination can be used. Through two examples and by means of simulation we investigate some properties of the screening step. In the simulation study we consider situations with fifteen and 25 variables, respectively, of which seven have an influence on the outcome. With the screening step most of the uninfluential variables will be eliminated, but also some variables with a weak effect. Variable screening leads to more applicable models without eliminating models, which are more strongly supported by the data. Furthermore, we give recommendations for important parameters of the screening step.     

Bayesian covariance matrix estimation using a mixture of decomposable graphical models

We present a Bayesian approach to estimating a covariance matrix by using a prior that is a mixture over all decomposable graphs, with the probability of each graph size specified by the user and graphs of equal size assigned equal probability. Most previous approaches assume that all graphs are equally probable. We show empirically that the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs in more efficiently estimating the covariance matrix. The prior requires knowing the number of decomposable graphs for each graph size and we give a simulation method for estimating these counts. We also present a Markov chain Monte Carlo method for estimating the posterior distribution of the covariance matrix that is much more efficient than current methods. Both the prior and the simulation method to evaluate the prior apply generally to any decomposable graphical model.     

零膨胀计数数据的联合建模及变量选择

零膨胀计数数据破坏了泊松分布的方差-均值关系，可由取值服从泊松分布的数据和取值为零(退化分布)的数据各占一定比例所构成的混合分布所解释。本文基于自适应弹性网技术， 研究了零膨胀计数数据的联合建模及变量选择问题.对于零膨胀泊松分布，引入潜变量，构造出零膨胀泊松模型的完全似然, 其中由零膨胀部分和泊松部分两项组成.考虑到协变量可能存在共线性和稀疏性，通过对似然函数加自适应弹性网惩罚得到目标函数,然后利用EM算法得到回归系数的稀疏估计量，并用贝叶斯信息准则BIC来确定最优调节参数.本文也给出了估计量的大样本性质的理论证明和模拟研究，最后把所提出的方法应用到实际问题中。     

Inference after variable selection using restricted permutation methods

When confronted with multiple covariates and a response variable, analysts sometimes apply a variable‐selection algorithm to the covariate‐response data to identify a subset of covariates potentially associated with the response, and then wish to make inferences about parameters in a model for the marginal association between the selected covariates and the response. If an independent data set were available, the parameters of interest could be estimated by using standard inference methods to fit the postulated marginal model to the independent data set. However, when applied to the same data set used by the variable selector, standard (“naive”) methods can lead to distorted inferences. The authors develop testing and interval estimation methods for parameters reflecting the marginal association between the selected covariates and response variable, based on the same data set used for variable selection. They provide theoretical justification for the proposed methods, present results to guide their implementation, and use simulations to assess and compare their performance to a sample‐splitting approach. The methods are illustrated with data from a recent AIDS study. The Canadian Journal of Statistics 37: 625–644; 2009 © 2009 Statistical Society of Canada     

一种增益可调CMOS恒带宽单片放大器

基于电流跟随器和负反馈原理，并结合电流镜像与虚地技术，得到了一种具有不依赖于闭环电压增益的１２０ｋＨｚ～８ＭＨｚ恒定带宽，增益０～６０ｄＢ可调，最高稳定工作频率５ＭＨｚ，功耗５．２ｍＷ的高性能ＣＭＯＳ放大器，其ＳＰＩＣＥ模拟表明，该放大器电气性能优越，模拟结果与理论分析比较吻合；可采用３～５μｍ硅栅ＣＭＯＳ工艺技术单片化集成实现，并可望用于宽带视频放大等模拟信号处理领域。     

Small-Sample Properties of GMM-Based Wald Tests

This article assesses the small-sample properties of generalized-method-of-moments-based Wald statistics by using (a) a vector white-noise process and (b) an equilibrium business-cycle model as the data-generating mechanisms. In many cases, the small-sample size of the Wald tests exceeds its asymptotic size and increases sharply with the number of hypotheses being jointly tested. We argue that this is mostly due to difficulty in estimating the spectral-density matrix of the residuals. Estimators of this matrix that impose restrictions implied by the model or the null hypothesis substantially improve the properties of the Wald statistics.     

Powerful Trend Function Tests That Are Robust to Strong Serial Correlation,With an Application to the Prebisch–Singer Hypothesis

We propose tests for hypotheses on the parameters of the deterministic trend function of a univariate time series. The tests do not require knowledge of the form of serial correlation in the data, and they are robust to strong serial correlation. The data can contain a unit root and still have the correct size asymptotically. The tests that we analyze are standard heteroscedasticity autocorrelation robust tests based on nonparametric kernel variance estimators. We analyze these tests using the fixed-b asymptotic framework recently proposed by Kiefer and Vogelsang. This analysis allows us to analyze the power properties of the tests with regard to bandwidth and kernel choices. Our analysis shows that among popular kernels, specific kernel and bandwidth choices deliver tests with maximal power within a specific class of tests. Based on the theoretical results, we propose a data-dependent bandwidth rule that maximizes integrated power. Our recommended test is shown to have power that dominates a related test proposed by Vogelsang. We apply the recommended test to the logarithm of a net barter terms of trade series and we find that this series has a statistically significant negative slope. This finding is consistent with the well-known Prebisch–Singer hypothesis.     

Partitioned cross-validation

Partitioned cross-validation is proposed as a method for overcoming the large amounts of across sample variability to which ordinary cross-validation is subject. The price for cutting down on the sample noise is that a type of bias is intriduced. A theory is presented for optimal trade-off of this variance and bias. Comparison with other bandwidth selection methods is given.     

On distribution function estimation with partially rank-ordered set samples: estimating mercury level in fish using length frequency data

We study the non-parametric estimation of a continuous distribution function F based on the partially rank-ordered set (PROS) sampling design. A PROS sampling design first selects a random sample from the underlying population and uses judgement ranking to rank them into partially ordered sets, without measuring the variable of interest. The final measurements are then obtained from one of the partially ordered sets. Considering an imperfect PROS sampling procedure, we first develop the empirical distribution function (EDF) estimator of F and study its theoretical properties. Then, we consider the problem of estimating F, where the underlying distribution is assumed to be symmetric. We also find a unique admissible estimator of F within the class of nondecreasing step functions with jumps at observed values and show the inadmissibility of the EDF. In addition, we introduce a smooth estimator of F and discuss its theoretical properties. Finally, we expand on various numerical illustrations of our results via several simulation studies and a real data application and show the advantages of PROS estimates over their counterparts under the simple random and ranked set sampling designs.