Multivariate linear regression with missing values

This contribution presents and discusses an efficient algorithm for multivariate linear regression analysis of data sets with missing values. The algorithm is based on the insight that multivariate linear regression can be formulated as a set of individual univariate linear regressions. All available information is used and the calculations are explicit. The only restriction is that the independent variable matrix has to be non-singular. There is no need for imputation of interpolated or otherwise guessed values which require subsequent iterative refinement.     

回归的能源有效网络大数据流汇聚算法研究

为了降低传感器网络数据流汇聚时的能源消耗,提出了一种基于回归的能源有效数据流汇聚算法。首先,将传感器节点分为活跃节点和能源有效节点。然后,以活跃节点为中心点将所有节点进行聚类,并应用回归方法通过活跃节点的数据流对能源有效节点的数据进行预测。接下来,通过节点预测值的累积误差不断修正活跃节点集。最后,应用活跃节点的数据流信息对能源有效节点的数据进行预测。实验表明,本文提出的算法与其它相关算法相比具有更好的预测准确性。     

Additive hazards regression with random effects for clustered failure times

Additive hazards model with random effects is proposed for modelling the correlated failure time data when focus is on comparing the failure times within clusters and on estimating the correlation between failure times from the same cluster, as well as the marginal regression parameters. Our model features that, when marginalized over the random effect variable, it still enjoys the structure of the additive hazards model. We develop the estimating equations for inferring the regression parameters. The proposed estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Furthermore, the estimator of the baseline hazards function is proposed and its asymptotic properties are also established. We propose a class of diagnostic methods to assess the overall fitting adequacy of the additive hazards model with random effects. We conduct simulation studies to evaluate the finite sample behaviors of the proposed estimators in various scenarios. Analysis of the Diabetic Retinopathy Study is provided as an illustration for the proposed method.     

Numerical discretization-based kernel type estimation methods for ordinary differential equation models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.     

Estimation of rating classes and default probabilities in credit risk models with dependencies

Let Y = m(X) + ε be a regression model with a dichotomous output Y and a one‐step regression function m . In the literature, estimators for the three parameters of m , that is, the breakpoint θ and the levels a and b , are proposed for independent and identically distributed (i.i.d.) observations. We show that these standard estimators also work in a non‐i.i.d. framework, that is, that they are strongly consistent under mild conditions. For that purpose, we use a linear one‐factor model for the input X and a Bernoulli mixture model for the output Y . The estimators for the split point and the risk levels are applied to a problem arising in credit rating systems. In particular, we divide the range of individuals' creditworthiness into two groups. The first group has a higher probability of default and the second group has a lower one. We also stress connections between the standard estimator for the cutoff θ and concepts prevalent in credit risk modeling, for example, receiver operating characteristic. Copyright © 2014 John Wiley & Sons, Ltd.     

An emerging strategy for tracing the anti-erectile dysfunction components of raw and salt-processed semens of Astragali Complanati by combinatory liquid chromatography–mass spectrometry-based quantitative analysis,efficacy assessment on impotent rats,and partial least squares regression

Semens of Astragali Complanati own anti-erectile dysfunction effect; however, the components which contribute to the anti-erectile dysfunction effect remain unclear. This work raised a strategy that integrates liquid chromatography coupled mass spectrometry-based quantitative analysis, anti-erectile dysfunction assessment on impotent rats, and their relationship analysis for pinpointing anti-erectile dysfunction components from semens of Astragali Complanati. For simultaneous quantification of seven major components in raw and salt-processed semens of Astragali Complanati, an accurate and reliable liquid chromatography–mass spectrometry method was developed under multiple reaction monitoring mode. Of note, chloramphenicol was employed as the internal standard. The method showed good linearity and repeatability, where the recovery rates of each component ranged from 98.1 to 104.7%, and the precisions of intra- and interday were all within 3.4%. The method has been used for quantification of the seven major components in 10 batches of raw and salt-processed semens of Astragali Complanati. Then, the anti-erectile dysfunction effects of raw and salt-processed semens of Astragali Complanati were evaluated on impotent rats. Gray relationship analysis and partial least squares regression were combined for elucidating the relationship. As a result, complanatuside, astragalin, complanatoside B, and kaempferol were found to be responsible for anti-erectile dysfunction effect of Astragali Complanati.