A study of partial F tests for multiple linear regression models

Partial F tests play a central role in model selections in multiple linear regression models. This paper studies the partial F tests from the view point of simultaneous confidence bands. It first shows that there is a simultaneous confidence band associated naturally with a partial F test. This confidence band provides more information than the partial F test and the partial F test can be regarded as a side product of the confidence band. This view point of confidence bands also leads to insights of the major weakness of the partial F tests, that is, a partial F test requires implicitly that the linear regression model holds over the entire range of the covariates in concern. Improved tests are proposed and they are induced by simultaneous confidence bands over restricted regions of the covariates. Power comparisons between the partial F tests and the new tests have been carried out to assess when the new tests are more or less powerful than the partial F tests. Computer programmes have been developed for easy implements of these new confidence band based inferential methods. An illustrative example is provided.     

Simultaneous confidence bands for all contrasts of three or more simple linear regression models over an interval

Simultaneous confidence intervals are used in Scheffé (1953) to assess any contrasts of several normal means. In this paper, the problem of assessing any contrasts of several simple linear regression models by using simultaneous confidence bands is considered. Using numerical integration, Spurrier (1999) constructed exact simultaneous confidence bands for all the contrasts of several regression lines over the whole range (−∞,∞) of the explanatory variable when the design matrices of the regression lines are all equal. In this paper, a simulation-based method is proposed to construct simultaneous confidence bands for all the contrasts of the regression lines when the explanatory variable is restricted to an interval and the design matrices of the regression lines may be different. The critical value calculated by this method can be as close to the exact critical value as required if the number of replications in the simulation is chosen sufficiently large. The methodology is illustrated with a real problem in which sizes of the left atrium of infants in three diagnostic groups (severely impaired, mildly impaired and normal) are compared.     

Approximate and generalized confidence bands for the mean and mode functions of the lognormal diffusion process

Approximate and generalized confidence bands for the mean and mode functions of the univariate lognormal diffusion process are obtained. To this end, the already existing methods for building confidence intervals for the mean of the lognormal distribution have been suitably adapted. Moreover, a new method has been proposed. The bands obtained from the above procedures are compared through a simulation study and the comparisons are made both in terms of coverage errors and average widths. This comparative study allows to choose the most appropriate confidence band for each particular case in practical situations. This is shown in an application to a real data set.     

Modelling of a surface marine vehicle with kernel ridge regression confidence machine

This paper describes the use of Kernel Ridge Regression (KRR) and Kernel Ridge Regression Confidence Machine (KRRCM) for black box identification of a surface marine vehicle. Data for training and test have been obtained from several manoeuvres typically used for marine system identification. Thus, a 20/20 degrees Zig-Zag, a 10/10 degrees Zig-Zag, and different evolution circles have been employed for the computation and validation of the model. Results show that the application of conformal prediction provides an accurate model that reproduces with large accuracy the actual behaviour of the ship with confidence margins that ensure that the model response is within these margins, making it a suitable tool for system identification.     

Robust estimation in multiple linear regression model with non-Gaussian noise

The traditional least squares estimators used in multiple linear regression model are very sensitive to design anomalies. To rectify the situation we propose a reparametrization of the model. We derive modified maximum likelihood estimators and show that they are robust and considerably more efficient than the least squares estimators besides being insensitive to moderate design anomalies.     

Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization

Some regularization methods, including the group lasso and the adaptive group lasso, have been developed for the automatic selection of grouped variables (factors) in conditional mean regression. In many practical situations, such a problem arises naturally when a set of dummy variables is used to represent a categorical factor and/or when a set of basis functions of a continuous variable is included in the predictor set. Complementary to these earlier works, the simultaneous and automatic factor selection is examined in quantile regression. To incorporate the factor information into regularized model fitting, the adaptive sup-norm regularized quantile regression is proposed, which penalizes the empirical check loss function by the sum of factor-wise adaptive sup-norm penalties. It is shown that the proposed method possesses the oracle property. A simulation study demonstrates that the proposed method is a more appropriate tool for factor selection than the adaptive lasso regularized quantile regression.     

回归—聚类联合框架下的手写文本行提取

目的 手写文本行提取是文档图像处理中的重要基础步骤,对于无约束手写文本图像,文本行都会有不同程度的倾斜、弯曲、交叉、粘连等问题。利用传统的几何分割或聚类的方法往往无法保证文本行边缘的精确分割。针对这些问题提出一种基于文本行回归-聚类联合框架的手写文本行提取方法。方法 首先,采用各向异性高斯滤波器组对图像进行多尺度、多方向分析,利用拖尾效应检测脊形结构提取文本行主体区域,并对其骨架化得到文本行回归模型。然后,以连通域为基本图像单元建立超像素表示,为实现超像素的聚类,建立了像素-超像素-文本行关联层级随机场模型,利用能量函数优化的方法实现超像素的聚类与所属文本行标注。在此基础上,检测出所有的行间粘连字符块,采用基于回归线的k-means聚类算法由回归模型引导粘连字符像素聚类,实现粘连字符分割与所属文本行标注。最后,利用文本行标签开关实现了文本行像素的操控显示与定向提取,而不再需要几何分割。结果 在HIT-MW脱机手写中文文档数据集上进行文本行提取测试,检测率DR为99.83%,识别准确率RA为99.92%。结论 实验表明,提出的文本行回归-聚类联合分析框架相比于传统的分段投影分析、最小生成树聚类、Seam Carving等方法提高了文本行边缘的可控性与分割精度。在高效手写文本行提取的同时,最大程度地避免了相邻文本行的干扰,具有较高的准确率和鲁棒性。     

计算机程序-多波长直线回归法测定牙周康胶囊中的甲硝唑和芬布芬

研究建立计算机程序一多波长直线回归法,以测定药品牙周康胶囊中甲硝唑和芬布芬的含量.在277.0 nm～318.0 nm波长范围内,选择42个波长点进行测定;采用计算机多波长直线回归程序计算;不经分离,直接测定牙周康胶囊中甲硝唑和芬布芬的含量.两者的平均回收率和相对标准偏差,分别为98.3%,0.75%和98.9%,1.0%.本方法简单、快速、准确、适用于控制牙周康胶囊的质量.     

On properties of predictors derived with a two-step bootstrap model averaging approach—A simulation study in the linear regression model

In many applications of model selection there is a large number of explanatory variables and thus a large set of candidate models. Selecting one single model for further inference ignores model selection uncertainty. Often several models fit the data equally well. However, these models may differ in terms of the variables included and might lead to different predictions. To account for model selection uncertainty, model averaging procedures have been proposed. Recently, an extended two-step bootstrap model averaging approach has been proposed. The first step of this approach is a screening step. It aims to eliminate variables with negligible effect on the outcome. In the second step the remaining variables are considered in bootstrap model averaging. A large simulation study is performed to compare the MSE and coverage rate of models derived with bootstrap model averaging, the full model, backward elimination using Akaike and Bayes information criterion and the model with the highest selection probability in bootstrap samples. In a data example, these approaches are also compared with Bayesian model averaging. Finally, some recommendations for the development of predictive models are given.     

The Koul-Susarla-Van Ryzin and weighted least squares estimates for censored linear regression model: A comparative study

The Koul-Susarla-Van Ryzin (KSV) and weighted least squares (WLS) methods are simple to use techniques for handling linear regression models with censored data. They do not require any iterations and standard computer routines can be employed for model fitting. Emphasis has been given to the consistency and asymptotic normality for both estimators, but the finite sample performance of the WLS estimator has not been thoroughly investigated. The finite sample performance of these two estimators is compared using an extensive simulation study as well as an analysis of the Stanford heart transplant data. The results demonstrate that the WLS approach performs much better than the KSV method and is reliable for use with censored data.     

An exponentially weighted moving average scheme with variable sampling intervals for monitoring linear profiles

This paper proposes an exponentially weighted moving average scheme with variable sampling intervals for monitoring linear profiles. A computer program in Fortran is available to assist in the design of the control chart and the algorithm of the Fortran program is also given. Some useful guidelines are also provided to aid users in choosing parameters for a particular application. Simulation results on the detection performance of the proposed control chart, compared with some other competing methods show that it provides quite robust and satisfactory performance in various cases, including intercept shifts, slope shifts and standard deviation shifts. A real data example from an optical imaging system is employed to illustrate the implementation and the use of the proposed control scheme.     

基于线性回归的无线传感器网络链路质量估计方法研究

针对无线传感器网络链路质量估计模型中回归算法复杂度高、缺少统一分类标准和公开数据集等问题,提出了一种基于EWMA和线性回归的链路质量估计方法ELR-LQE。以物理层获取的RSSI、LQI和SNR,以及包接收率PRR作为度量参数,分别在多种实验环境中采用不同的发射功率、竞争条件和部署方式采集数据,建立了链路质量估计数据集。通过最小值填充和EWMA对数据进行预处理,明显提高了回归模型的输入特征与链路质量的相关性。与现有方法相比,提出方法易于和网络层协议适配,并且复杂度较低,适合在资源有限的无线传感器网络节点中实现。实验结果显示,ELR-LQE具有较高的精度,在多种实验条件下平均的ME为4.6×10-2,R2为0.99。     

Estimation of a flexible simple linear model for interval data based on set arithmetic

The estimation of a simple linear regression model when both the independent and dependent variable are interval valued is addressed. The regression model is defined by using the interval arithmetic, it considers the possibility of interval-valued disturbances, and it is less restrictive than existing models. After the theoretical formalization, the least-squares (LS) estimation of the linear model with respect to a suitable distance in the space of intervals is developed. The LS approach leads to a constrained minimization problem that is solved analytically. The strong consistency of the obtained estimators is proven. The estimation procedure is reinforced by a real-life application and some simulation studies.     

A new a priori SNR estimator based on multiple linear regression technique for speech enhancement

We propose a new approach to estimate the a priori signal-to-noise ratio (SNR) based on a multiple linear regression (MLR) technique. In contrast to estimation of the a priori SNR employing the decision-directed (DD) method, which uses the estimated speech spectrum in previous frame, we propose to find the a priori SNR based on the MLR technique by incorporating regression parameters such as the ratio between the local energy of the noisy speech and its derived minimum along with the a posteriori SNR. In the experimental step, regression coefficients obtained using the MLR are assigned according to various noise types, for which we employ a real-time noise classification scheme based on a Gaussian mixture model (GMM). Evaluations using both objective speech quality measures and subjective listening tests under various ambient noise environments show that the performance of the proposed algorithm is better than that of the conventional methods.     

A parallel approach for determining confidence intervals of variable statistics in large and sparse linear equations with RHS ranges

This study proposes an algorithm capable of working in parallel for solving variable statistics with large and sparse linear equations under given right hand side ranges. A comparative study to the direct linear programming method is conducted under a main central processor and up to four parallel processors. The studied results are reported computationally and discussed. Moreover, the approach can be adapted for the system under domain decompositions structure leading to a better efficiency experimentally in a case example.     

Testing for two components in a switching regression model

Switching regression models form a suitable model class for regression problems with unobserved heterogeneity. A basic issue encountered in applications of switching regression models is to choose the number of states of the switching regime. Based on the modified likelihood ratio test (LRT) statistic a test for two against more states of the regime is proposed, and its asymptotic distribution is derived in the case when there is a single switching parameter. Further, it is shown that the asymptotic distribution of the test remains unchanged if the regime is Markov dependent. A simulation study illustrates the finite-sample behavior of the test. Finally, the methodology is applied to the data of a dental health trial. In this case the model selection criteria AIC and BIC favor distinct binomial regression models with switching intercepts (AIC three states, BIC two states). The modified LRT allows us to reject the null hypothesis of two states in favor of three states.     

Neural networks for bandwidth selection in local linear regression of time series

The problem of automatic bandwidth selection in nonparametric regression is considered when a local linear estimator is used to derive nonparametrically the unknown regression function. A plug-in method for choosing the smoothing parameter based on the use of the neural networks is presented. The method applies to dependent data generating processes with nonlinear autoregressive time series representation. The consistency of the method is shown in the paper, and a simulation study is carried out to assess the empirical performance of the procedure.     

非授权频段长期演进系统中的混合动态分簇算法

针对非授权频段长期演进（LTE）系统中动态子帧配置引起的交叉子帧干扰问题,提出了一种综合考虑大尺度损耗及小区业务量情况的混合动态分簇算法。首先,通过基站端对大尺度损耗及小区业务量情况的周期性测量,计算出对应的相关度值;然后,根据相关度值对小区进行轮询式分簇,实现小区分簇结果的周期性更新;最后,根据更新后的小区分簇结果执行动态子帧配置。仿真实验中,相比传统的静态分簇算法,中业务到达率条件下混合动态分簇算法的用户上下行平均吞吐量分别提升了约16.92%和34.33%;用户上下行平均时延分别降低了约14.18%和36.32%。仿真结果表明,混合动态分簇算法可以有效减小交叉子帧干扰的影响,提升系统吞吐量,性能优于传统的静态分簇算法。     

An optimal parallel algorithm for sparse matrix bandwidth reduction on a linear array

A simple and efficient algorithm for the bandwidth reduction of sparse symmetric matrices is proposed. It involves column-row permutations and is well-suited to map onto the linear array topology of the SIMD architectures. The efficiency of the algorithm is compared with the other existing algorithms. The interconnectivity and the memory requirement of the linear array are discussed and the complexity of its layout area is derived. The parallel version of the algorithm mapped onto the linear array is then introduced and is explained with the help of an example. The optimality of the parallel algorithm is proved by deriving the time complexities of the algorithm on a single processor and the linear array.     

Least trimmed euclidean deviations for robust leverage in regression estimates

Usually, in the regression models, the data are contaminated with unusually observations (outliers). For that reason the last 30 years have developed robust regression estimators. Among them some of the most famous are Least Trimmed Squares (LTS), MM, Penalized Trimmed Square (PTS) and others. Most of these methods, especially PTS, are based on initial leverage, concerning x outlying observations, of the data sample. However, often, multiple x-outliers pull the distance towards their value, causing leverage bias, and this is the masking problem.In this work we develop a new algorithm for robust leverage estimate based on Least Trimmed Euclidean Deviations (LTED). Extensive computational, Monte-Carlo simulations, with varying types of outliers and degrees of contamination, indicate that the LTED procedure identifies successfully the multiple outliers, and the resulting robust leverage improves significantly the PTS performance.