Variable Selection of Partially Linear Single-index Models

In this article, we study the variable selection of partially linear single-index model(PLSIM). Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average variance with adaptive l1 penalty. Implementation algorithm is given. Under some regular conditions, we demonstrate the oracle properties of aLASSO procedure for PLSIM. Simulations are used to investigate the effectiveness of the proposed method for variable selection of PLSIM.

ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA

In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.

Empirical Likelihood Inference for Generalized Partially Linear Models with Longitudinal Data

In this article, we propose a generalized empirical likelihood inference for the parametric component in semiparametric generalized partially linear models with longitudinal data. Based on the extended score vector, a generalized empirical likelihood ratios function is defined, which integrates the within-cluster?correlation meanwhile avoids direct estimating the nuisance parameters in the correlation matrix. We show that the proposed statistics are asymptotically?Chi-squared under some suitable conditions, and hence it can be used to construct the confidence region of parameters. In addition, the maximum empirical likelihood estimates of parameters and the corresponding asymptotic normality are obtained. Simulation studies demonstrate the performance of the proposed method.

Sieve MLE for Generalized Partial Linear Models with Type Ⅱ Interval-censored Data

This article concerded with a semiparametric generalized partial linear model （GPLM） with the type Ⅱ censored data. A sieve maximum likelihood estimator （MLE） is proposed to estimate the parameter component, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically normal and efficient, and the estimator of the nonparametric function has an optimal convergence rate.

Testing Equality of Nonparametric Functions in Two Partially Linear Models

We propose the test statistic to check whether the nonpararnetric functions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alternative by the local linear method, where we ignore the parametric components, and then estimate the parameters by the two stage method. The test statistic is derived, and it is shown to be asymptotically normal under the null hypothesis.

Finite Mixture of Heteroscedastic Single-Index Models

In many applications a heterogeneous population consists of several subpopulations. When each subpopulation can be adequately modeled by a heteroscedastic single-index model, the whole population is characterized by a finite mixture of heteroscedastic single-index models. In this article, we propose an estimation algorithm for fitting this model, and discuss the implementation in detail. Simulation studies are used to demonstrate the performance of the algorithm, and a real example is used to illustrate the application of the model.

Testing Linearity of Nonparametric Component in Partially Linear Model

In this paper, we propose the test statistic to check whether the nonparametric function in partially linear models is linear or not. We estimate the nonparametric function in alternative by using the local linear method, and then estimate the parameters by the two stage method. The test statistic under the null hypothesis is calculated, and it is shown to be asymptotically normal.

Tests for nonparametric parts on partially linear single index models

Tests for nonparametric parts on partially linear single index models are considered in this paper. Based on the estimates obtained by the local linear method, the generalized likelihood ratio tests for the models are established. Under the null hypotheses the normalized tests follow asymptotically the χ2-distribution with the scale constants and the degrees of freedom being independent of the nuisance parameters, which is called the Wilks phenomenon. A simulated example is used to evaluate the performances of the testing procedures empirically.

典型水蚀区坡耕地黑土质量的空间分异特征及影响因素

[目的]为明确侵蚀—沉积在黑土坡耕地土壤质量空间分异格局中的塑造作用。[方法]以东北典型水蚀区坡耕地为研究对象,利用110个样点的土壤属性,采用基于最小数据集的土壤质量指数(SQI)指标,评价坡面尺度土壤质量的空间分异特征,并利用广义线性模型(GLM)明确坡度、坡位、土层深度等因子对土壤质量的贡献。[结果](1)坡耕地土壤养分含量和空间特征在耕作层和亚表层间呈相反规律。对于大部分养分指标,耕作层的含量显著高于亚表层,但是,其空间异质性及土壤养分含量间的相关性低于亚表层(p<0.05);(2)侵蚀沉积作用影响坡耕地土壤质量的空间分布特征。SQI在强烈侵蚀的坡中显著低于轻度侵蚀的坡上和沉积区的坡下(p<0.05),与坡上相比,坡中SQI在耕作层和亚表层分别降低26.2%和31.6%,沉积作用并不一定提高强烈侵蚀坡耕地沉积区的土壤质量,坡下和坡上耕作层的土壤质量无显著差异(p>0.05);(3)土层深度、坡位和坡度是坡耕地SQI变异的主要影响因素。GLM结果显示,对于同一个土壤层次,坡度、坡位及其交互作用对SQI变异的解释度达95%,其中,坡位和坡度的解释度分别为68%和22%;考虑土壤深度因素,在0—40 cm土层,土层深度、坡位和坡度对SQI变异的解释度分别为39%,31%和10%。[结论]采用SQI和GLM相结合的方法,明确侵蚀—沉积过程在坡耕地黑土质量空间分异中的塑造作用,研究成果可为典型水蚀区侵蚀退化黑土地质量评价和管理提供技术支撑。

Variable Selection for Generalized Linear Model with Highly Correlated Covariates

The penalized variable selection methods are often used to select the relevant covariates and estimate the unknown regression coefficients simultaneously,but these existing methods may fail to be consistent for the setting with highly correlated covariates.In this paper,the semi-standard partial covariance(SPAC)method with Lasso penalty is proposed to study the generalized linear model with highly correlated covariates,and the consistencies of the estimation and variable selection are shown in high-dimensional settings under some regularity conditions.Some simulation studies and an analysis of colon tumor dataset are carried out to show that the proposed method performs better in addressing highly correlated problem than the traditional penalized variable selection methods.

Statistical inference on parametric part for partially linear single-index model

Statistical inference on parametric part for the partially linear single-index model (PLSIM) is considered in this paper. A profile least-squares technique for estimating the parametric part is proposed and the asymptotic normality of the profile least-squares estimator is given. Based on the estimator, a generalized likelihood ratio (GLR) test is proposed to test whether parameters on linear part for the model is under a contain linear restricted condition. Under the null model, the proposed GLR statistic follows asymptotically the χ2-distribution with the scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Both simulated and real data examples are used to illustrate our proposed methods.

Empirical likelihood confidence regions of the parameters in a partially linear single-index model

In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.

Generalized F-Test for High Dimensional Regression Coefficients of Partially Linear Models

This paper proposes a test procedure for testing the regression coefficients in high dimensional partially linear models based on the F-statistic. In the partially linear model, the authors first estimate the unknown nonlinear component by some nonparametric methods and then generalize the F-statistic to test the regression coefficients under some regular conditions. During this procedure, the estimation of the nonlinear component brings much challenge to explore the properties of generalized F-test. The authors obtain some asymptotic properties of the generalized F-test in more general cases,including the asymptotic normality and the power of this test with p/n ∈(0, 1) without normality assumption. The asymptotic result is general and by adding some constraint conditions we can obtain the similar conclusions in high dimensional linear models. Through simulation studies, the authors demonstrate good finite-sample performance of the proposed test in comparison with the theoretical results. The practical utility of our method is illustrated by a real data example.

ROBUST ESTIMATION IN PARTIAL LINEAR MIXED MODEL FOR LONGITUDINAL DATA

In this article, robust generalized estimating equation for the analysis of partial linear mixed model for longitudinal data is used. The authors approximate the nonparametric function by a regression spline. Under some regular conditions, the asymptotic properties of the estimators are obtained. To avoid the computation of high-dimensional integral, a robust Monte Carlo Newton-Raphson algorithm is used. Some simulations are carried out to study the performance of the proposed robust estimators. In addition, the authors also study the robustness and the efficiency of the proposed estimators by simulation. Finally, two real longitudinal data sets are analyzed.

A Note on the Optimality of Generalized Cross-validation Bandwidth Selection in Partially Linear Models with Kernel Smoothing Estimator

The issue of selection of bandwidth in kernel smoothing method is considered within the context of partially linear models, hi this paper, we study the asymptotic behavior of the bandwidth choice based on generalized cross-validation （CCV） approach and prove that this bandwidth choice is asymptotically optimal. Numerical simulation are also conducted to investigate the empirical performance of generalized cross-valldation.

ZERO FINITE-ORDER SERIAL CORRELATION TEST IN A PARTIALLY LINEAR SINGLE-INDEX MODEL

这份报纸的目的是在一个部分线性的单个索引的模型测试内在的连续关联。在温和条件下面，当在错误条款没有连续关联时，建议测试统计被显示 asymptotically 有标准 chisquared 分发。说明他们的有限样品性质，模拟实验，以及一个真实数据例子，也被提供。建议测试统计的有限样品表演以估计的尺寸和力量是令人满意的，这被揭示。

A Thermal-Hydraulic Coolant Channel Module (CCM) for Single- and Two-Phase Flow

A theoretical “drift-flux based thermal-hydraulic mixture-fluid coolant channel model” is presented. It is the basis to a corresponding digital “Coolant Channel Module (CCM)”. This purpose derived “Separate-Region Mixture Fluid Approach” should yield an alternative platform to the currently dominant “Separate-Phase Models” where each phase is treated separately. Contrary to it, a direct procedure could be established with the objective to simulate in an as general as possible way the steady state and transient behaviour of characteristic parameters of single- and/or (now non-separated) two-phase fluids flowing within any type of heated or non-heated coolant channels. Their validity could be confirmed by a wide range of verification and validation runs, showing very satisfactory results. The resulting universally applicable code package CCM should provide a fundamental element for the simulation of thermal-hydraulic situations over a wide range of complex systems (such as different types of heat exchangers and steam generators as being applied in both conventional but also nuclear power stations, 1D and 3D nuclear reactor cores etc). Thereby the derived set of equations for different coolant channels (distinguished by their key numbers) as appearing in these systems can be combined with other ODE-s and non-linear algebraic relations from additional parts of such an overall model. And these can then to be solved by applying an appropriate integration routine. Within the solution procedure, however, mathematical discontinuities can arise. This due to the fact that along such a coolant channel transitions from single- to two-phase flow regimes and vice versa could take place. To circumvent these difficulties it will in the presented approach be proposed that the basic coolant channel (BC) is subdivided into a number of sub-channels (SC-s), each of them being occupied exclusively by only a single or a two-phase flow regime. After an appropriate nodalization of the BC (and thus its SC-s) and after applying a “modified finite volume method” together with other special activities the fundamental set of non-linear thermal-hydraulic partial differential equations together with corresponding constitutive relations can be solved for each SC separately. As a result of such a spatial discretization for each SC type (and thus the entire BC) the wanted set of non-linear ordinary differential equations of 1st order could be established. Obviously, special attention had to be given to the varying SC entrance or outlet positions, describing the movement of boiling boundaries or mixture levels along the channel. Including even the possibility of SC-s to disappear or be created anew during a transient.

Analysis of fMRI Single Subject Data in the Fourier Domain Acquired Using a Multiple Input Stimulus Experimental Design

Analysis of functional MRI (fMRI) blood oxygenation level dependent (BOLD) data is typically carried out in the time domain where the data has a high temporal correlation. These analyses usually employ parametric models of the hemodynamic response function (HRF) where either pre-whitening of the data is attempted or autoregressive (AR) models are employed to model the noise. Statistical analysis then proceeds via regression of the convolution of the HRF with the input stimuli. This approach has limitations when considering that the time series collected are embedded in a brain image in which the AR model order may vary and pre-whitening techniques may be insufficient for handling faster sampling times. However fMRI data can be analyzed in the Fourier domain where the assumptions made as to the structure of the noise can be less restrictive and hypothesis tests are straightforward for single subject analysis, especially useful in a clinical setting. This allows for experiments that can have both fast temporal sampling and event-related designs where stimuli can be closely spaced in time. Equally important, statistical analysis in the Fourier domain focuses on hypothesis tests based on nonparametric estimates of the hemodynamic transfer function (HRF in the frequency domain). This is especially important for experimental designs involving multiple states (drug or stimulus induced) that may alter the form of the response function. In this context a univariate general linear model in the Fourier domain has been applied to analyze BOLD data sampled at a rate of 400 ms from an experiment that used a two-way ANOVA design for the deterministic stimulus inputs with inter-stimulus time intervals chosen from Poisson distributions of equal intensity.

函数型部分线性单指标空间自回归模型

该文提出了函数型部分线性单指标空间自回归模型,该模型综合并拓展了函数型单指标模型和空间自回归模型.基于拟极大似然估计(QMLE)和局部线性方法,构造了一个四阶段估计器来估计参数和非参数分量,并由假设条件给出了参数和非参数分量估计的渐近性质.在此基础上,通过Monte Carlo模拟研究了估计器的有限样本性能,最后对加拿大气象数据的年总降雨量和日均气温曲线建立了函数型单指标空间自回归模型,研究发现年总降雨量存在负向空间自相关性,日均气温与年总降雨量正相关.