变换法在解微分方程中的应用

变量代换法是解常微分方程的一种辅助方法，它能使问题简化．本文通过联系实例给出了变换在求解微分方程中的具体应用。     

Adaptive tests of regression functions via multiscale generalized likelihood ratios

Many applications of nonparametric tests based on curve estimation involve selecting a smoothing parameter. The author proposes an adaptive test that combines several generalized likelihood ratio tests in order to get power performance nearly equal to whichever of the component tests is best. She derives the asymptotic joint distribution of the component tests and that of the proposed test under the null hypothesis. She also develops a simple method of selecting the smoothing parameters for the proposed test and presents two approximate methods for obtaining its P‐value. Finally, she evaluates the proposed test through simulations and illustrates its application to a set of real data.     

基于广义第二价格拍卖的多级带宽定价模型

在差异化服务机制的基础上，研究了互联网的多级带宽定价问题．通过导入广义第二价格拍卖，构造了基于差异化服务的互联网多级带宽定价模型．该模型能够有效地解决Internet拥塞问题，促进网络资源的合理利用．     

二维变系数线性微分系统的求解定理

给出二维变系数线性微分系统在已知某解的情形下求通解的公式,并直接应用此公式,导出几类二维变系数线性微分系统的通解公式.对理论和实际应用都是有益的.     

Testing Inference in Inflated Beta Regressions under Model Misspecification

We consider testing inference in inflated beta regressions subject to model misspecification. In particular, quasi-z tests based on sandwich covariance matrix estimators are described and their finite sample behavior is investigated via Monte Carlo simulations. The numerical evidence shows that quasi-z testing inference can be considerably more accurate than inference made through the usual z tests, especially when there is model misspecification. Interval estimation is also considered. We also present an empirical application that uses real (not simulated) data.     

Quadratic Approximation via the SCAD Penalty with a Diverging Number of Parameters

The high-dimensional data arises in diverse fields of sciences, engineering and humanities. Variable selection plays an important role in dealing with high dimensional statistical modelling. In this article, we study the variable selection of quadratic approximation via the smoothly clipped absolute deviation (SCAD) penalty with a diverging number of parameters. We provide a unified method to select variables and estimate parameters for various of high dimensional models. Under appropriate conditions and with a proper regularization parameter, we show that the estimator has consistency and sparsity, and the estimators of nonzero coefficients enjoy the asymptotic normality as they would have if the zero coefficients were known in advance. In addition, under some mild conditions, we can obtain the global solution of the penalized objective function with the SCAD penalty. Numerical studies and a real data analysis are carried out to confirm the performance of the proposed method.     

Infill asymptotics for adaptive kernel estimators of spatial intensity

We apply the Abramson principle to define adaptive kernel estimators for the intensity function of a spatial point process. We derive asymptotic expansions for the bias and variance under the regime that n independent copies of a simple point process in Euclidean space are superposed. The method is illustrated by means of a simple example and applied to tornado data.     

Transductive versions of the LASSO and the Dantzig Selector

Transductive methods are useful in prediction problems when the training dataset is composed of a large number of unlabeled observations and a smaller number of labeled observations. In this paper, we propose an approach for developing transductive prediction procedures that are able to take advantage of the sparsity in the high dimensional linear regression. More precisely, we define transductive versions of the LASSO (Tibshirani, 1996) and the Dantzig Selector (Candès and Tao, 2007). These procedures combine labeled and unlabeled observations of the training dataset to produce a prediction for the unlabeled observations. We propose an experimental study of the transductive estimators that shows that they improve the LASSO and Dantzig Selector in many situations, and particularly in high dimensional problems when the predictors are correlated. We then provide non-asymptotic theoretical guarantees for these estimation methods. Interestingly, our theoretical results show that the Transductive LASSO and Dantzig Selector satisfy sparsity inequalities under weaker assumptions than those required for the “original” LASSO.     

Statistical estimation of internal available bandwidth

This paper presents a method for using end-to-end available bandwidth measurements in order to estimate available bandwidth on individual internal links. The basic approach is to use a power transform on the observed end-to-end measurements, model the result as a mixture of spatially correlated exponential random variables, carryout estimation by moment methods, then transform back to the original variables to get estimates and confidence intervals for the expected available bandwidth on each link. Because spatial dependence leads to certain parameter confounding, only upper bounds can be found reliably. Simulations with ns2 show that the method can work well and that the assumptions are approximately valid in the examples.