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Subset selection by Mallows C_p: A mixed integer programming approach

EXPERT SYSTEMS WITH APPLICATIONS 2015年第1期42卷 325-331页

作者： Miyashiro, Ryuhei Takano, Yuichi Tokyo Univ Agr & Technol Inst Engn Dept Comp & Informat Sci Koganei Tokyo 1848588 Japan Tokyo Inst Technol Grad Sch Decis Sci & Technol Dept Ind Engn & Management Meguro Ku Tokyo 1528552 Japan

This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model. Employing Mallows' C-p, as a goodness-of-fit measure, we formulate the subset selection problem as a mixed integer quadratic programming problem. Computational results demonstrate that our method provides the best subset of variables in a few seconds when the number of candidate explanatory variables is less than 30. Furthermore, when handling datasets consisting of a large number of samples, it finds better-quality solutions faster than stepwise regression methods do. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Subset selection Mixed integer programming Mallows' C-p linear regression model

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A Methodology for Sensitivity Analysis Based on regression: Applications to Handle Uncertainty in Natural Resources Characterization

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NATURAL RESOURCES RESEARCH 2015年第3期24卷 239-274页

作者： Zagayevskiy, Yevgeniy Deutsch, Clayton V. Univ Alberta Dept Civil & Environm Engn Sch Min & Petr Engn CCGMarkin CNRL Nat Resources Engn Facil Edmonton AB T6G 2W2 Canada

Uncertainty in a natural resource model represents risk that should be minimized for improved management. Natural resources are components of complex earth science systems, which can be exhaustively sampled, numerically modeled with Monte Carlo simulation, or both, to understand their underlying nature. A numerical model represents relationships between a response variable and predictor variables. Uncertainty in a response variable can be observed directly, but understanding the importance of each predictor variable requires further post-processing of the numerical model. A methodology of local sensitivity analysis, based on linear and quadratic regression models, is developed to help understand the uncertainty contribution of each predictor variable to the response model. Sensitivity coefficients, predicted response values, and summary statistics with model utility tests for the regression models are evaluated. The importance of standardized sensitivity coefficients and other measures are developed. Standardized sensitivity coefficients represent the contribution of uncertainty in the predictor variables to uncertainty in model response. Results of the sensitivity analysis are visually summarized in the form of extended tornado charts. The proposed methodology is applied to representative petroleum and mining case studies. The methodology is robust, efficient, descriptive, and straightforward. Understanding of the contribution of each predictor variable to the response variable is useful for minimization of model response uncertainty, decision-making, and further study.

关键词： Local sensitivity analysis Sensitivity coefficients Tornado chart linear regression model Quadratic regression model

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Multivariate analysis of determinants of Internet banking use in European Union countries

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CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2015年第3期23卷 563-578页

作者： Dumicic, Ksenija Casni, Anita Ceh Palic, Irena Univ Zagreb Fac Econ & Business Zagreb 41000 Croatia

The main objective of the paper is to analyse the determinants of Internet banking use in European Union countries based on EUROSTAT data for 2011. The considered determinants of Internet banking use are selected in line with relevant theoretical and empirical research and submitted to factor analysis which yielded two factors. The first extracted factor comprises Information and Communication Technology (ICT) infrastructure, i.e. broadband penetration rate and level of Internet access. The second factor comprises individuals' level of Internet skills and GDP per capita. On the basis of the two mentioned factors, European Union countries are grouped into two clusters using cluster analysis. In order to analyse the impact of selected variables, a multiple regression analysis of Internet banking use is performed using extracted factors as independent variables. The regression analysis shows that an increase in ICT infrastructure leads to an increase in Internet banking use.

关键词： Internet banking use European Union countries Cluster analysis Factor analysis Information and communications technology (ICT) linear regression model

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Detection of Moving Target and Localization of Clutter Using Doppler Radar on Mobile Platform

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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS 2015年第5期12卷 1156-1160页

作者： Kim, Youngwook Sekhon, Satbir S. Calif State Univ Fresno Dept Elect & Comp Engn Fresno CA 93740 USA

This letter explores the possibilities of detecting a moving target and localizing clutter using nonstationary Doppler radar. The detection of a moving target, particularly a human, has many potential applications in the fields of surveillance and rescue. In dangerous environments, Doppler radar can be used to effectively collect information about the surroundings, even through walls. However, a moving platform makes the detection of a moving target complicated due to Doppler shift caused by the clutter. We analyze the pattern of the Doppler shift due to clutter over time and develop a linear regression model that describes this pattern. The location of clutter can be estimated by the model with the time history of the measured Doppler shifts. Although the pattern from clutter follows the mathematical model, the pattern from a moving target does not, resulting in a high-percentage root-mean-square (RMS) fitting error. On the basis of the percentage RMS fitting error, a moving target is differentiated from clutter.

关键词： Doppler radar joint time-frequency analysis linear regression model moving target detection

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Increasing sorption isotherms accuracy: Weibull modelling and linear regression

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ENERGY EXPLORATION & EXPLOITATION 2015年第4期33卷 515-532页

作者： Dinis, M. A. P. Rodrigues, C. F. de Sousa, M. J. Lemos Fernando Pessoa Univ UFP UFP Energy Environm & Hlth Res Unit FP ENAS Energy Environm & Environm & Publ Hlth Res Labs 3 P-4249004 Oporto Portugal Acad Ciencias Lisboa P-1249122 Lisbon Portugal

Relying on an adequate mathematical approach, two different mathematical procedures can be applied to the huge database produced during gas sorption isotherm experiments in order to obtain accurate data to be used in the industrial practice. To treat data determined from gas sorption isotherms without a careful mathematical support will produce inaccurate results, because all the determinations will be dependent on human decision. The minimum error reported since the first stage of a sorption isotherm determination, which corresponds to volume calibrations of reference and sample cells performed through the use of helium, will produce enormous inaccuracies on sorption isotherm behavior. These inaccurate behaviors may sometimes invalidate any Coalbed Methane recovery and CO2 injection programs. The study consisted on investigating gas sorption isotherm accuracies determined during the first part of the sorption process, which is mainly conducted by monitoring the pressure decline with time, in the reference and the sample cells (when both cells are not in contact), until the stabilization stage is achieved. Three samples from two different coals were selected in order to study their gas sorption behavior, in terms of a clear mathematical approach, when submitted to three different gas compositions, viz. 99.999% methane (CH4);99.999% carbon dioxide (CO2);and a gas mixture containing 74.99% CH4 + 19.99% CO2 + 5.02% nitrogen (N-2). Sorption experiments allow to conclude that the three samples present the same mathematical response during the first part of the sorption process. However, all gas sorption data (adsorption and desorption) collected from reference cell have a better fitting to a Modified Weibull model, and all gas sorption data (adsorption and desorption) collected from sample cell respond in a trustworthy way to a linear regression model. Confidence bands and prediction intervals (or bands) were also computed.

关键词： Sorption isotherms Modified Weibull model linear regression model Confidence bands Prediction intervals

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Research on Correlation Analysis between Test Score and Classroom Attendance Based on linear regression model

Research on Correlation Analysis between Test Score and Clas...

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2010 The 2nd International Conference on Industrial Mechatronics and Automation (ICIMA 2010)

作者： Chengcheng Zhang Foreign Language Teaching & Researching Department College of Foreign Languages Hebei University Baoding,China Fei Wang Department of Electrical Engineering Science & Technology College North China Electric Power University Baoding,China

Test score is the main criteria to measure the learning effort of *** are many factors may improve or lower the test score or examination results,such as classroom attendance,home work,communication and interaction,teaching methods,self-learning,review,discussion,*** is very important to teachers and students to figure out the inherent correlation between test score and these *** this paper,a research on correlation analysis between test score and classroom attendance based on linear regression model is *** analysis is introduced and the curves of correlation between test score and classroom attendance are ploted based on the test score and classroom attendance records during two *** scatter diagram and linear regression model of three courses indicate that the test score or examination results closely related to the classroom attendance.

关键词： correlation analysis test score classroom attendance linear regression model

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Empirical Likelihood for Censored linear regression and Variable Selection

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SCANDINAVIAN JOURNAL OF STATISTICS 2015年第3期42卷 798-812页

作者： Wu, Tong Tong Li, Gang Tang, Chengyong Univ Rochester Dept Biostat & Computat Biol Rochester NY 14627 USA Univ Calif Los Angeles Dept Biostat Los Angeles CA 90024 USA Temple Univ Fox Sch Business Dept Stat Philadelphia PA 19122 USA

The linear regression model for right censored data, also known as the accelerated failure time model using the logarithm of survival time as the response variable, is a useful alternative to the Cox proportional hazards model. Empirical likelihood as a non-parametric approach has been demonstrated to have many desirable merits thanks to its robustness against model misspecification. However, the linear regression model with right censored data cannot directly benefit from the empirical likelihood for inferences mainly because of dependent elements in estimating equations of the conventional approach. In this paper, we propose an empirical likelihood approach with a new estimating equation for linear regression with right censored data. A nested coordinate algorithm with majorization is used for solving the optimization problems with non-differentiable objective function. We show that the Wilks' theorem holds for the new empirical likelihood. We also consider the variable selection problem with empirical likelihood when the number of predictors can be large. Because the new estimating equation is non-differentiable, a quadratic approximation is applied to study the asymptotic properties of penalized empirical likelihood. We prove the oracle properties and evaluate the properties with simulated data. We apply our method to a Surveillance, Epidemiology, and End Results small intestine cancer dataset.

关键词： accelerated failure time model coordinate descent algorithm high-dimensional data analysis linear regression model oracle property variable selection Wilks' theorem

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An optimal proportion of mixing broad-leaved forest for enhancing the effective productivity of moso bamboo

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ECOLOGY AND EVOLUTION 2015年第8期5卷 1576-1584页

作者： Cheng, Xiao-Fei Shi, Pei-Jian Hui, Cang Wang, Fu-Sheng Liu, Guo-Hua Li, Bai-Lian Nanjing Forestry Univ Collaborat Innovat Ctr Sustainable Forestry South Bamboo Res Inst Nanjing 210037 Jiangsu Peoples R China Univ Stellenbosch Dept Math Sci Ctr Invas Biol ZA-7602 Matieland South Africa African Inst Math Sci Math & Phys Biosci ZA-7945 Cape Town South Africa Univ Calif Riverside Dept Bot & Plant Sci Ecol Complex & Modeling Lab Riverside CA 92521 USA

Moso bamboos (Phyllostachys edulis) are important forestry plants in southern China, with substantial roles to play in regional economic and ecological systems. Mixing broad-leaved forests and moso bamboos is a common management practice in China, and it is fundamental to elucidate the interactions between broad-leaved trees and moso bamboos for ensuring the sustainable provision of ecosystem services. We examine how the proportion of broad-leaved forest in a mixed managed zone, topology, and soil profile affects the effective productivity of moso bamboos (i.e., those with significant economic value), using linear regression and generalized additive models. Bamboo's diameter at breast height follows a Weibull distribution. The importance of these variables to bamboo productivity is, respectively, slope (25.9%), the proportion of broad-leaved forest (24.8%), elevation (23.3%), gravel content by volume (16.6%), slope location (8.3%), and soil layer thickness (1.2%). Highest productivity is found on the 25 degrees slope, with a 600-m elevation, and 30% broad-leaved forest. As such, broad-leaved forest in the upper slope can have a strong influence on the effective productivity of moso bamboo, ranking only after slope and before elevation. These factors can be considered in future management practice.

关键词： Biomass environmental factors generalized additive model linear regression model productivity

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Estimating the model with Fixed and Random Effects by a Robust Method

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METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY 2015年第4期17卷 999-1014页

作者： Visek, Jan Amos Charles Univ Prague Inst Econ Studies Fac Social Sci Prague Czech Republic

regression model with fixed and random effects estimated by modified versions of the Ordinary Least Squares (OLS) is a standard tool of panel data analysis. However, it is vulnerable to the bad effects of influential observations (contamination and/or atypical observations). The paper offers robustified versions of the classical methods for this framework. The robustification is carried out by the same idea which was employed when robustifying OLS, it is the idea of weighting down the large order statistics of squared residuals. In contrast to the approach based on the M-estimators this approach does not need the studentization of residuals to reach the scale- and regression-equivariance of estimator in question. Moreover, such approach is not vulnerable with respect the inliers. The numerical study reveals the reliability of the respective algorithm. The results of this study were collected in a file which is possible to find on web, address is given below. Patterns of these results were included also into the paper. The possibility to reach nearly the full efficiency of estimation - due to the iteratively tailored weight function - in the case when there are no influential points is also demonstrated.

关键词： linear regression model The least weighted squares Fixed and random effects Numerical simulations

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modelling count response variables in informetric studies: Comparison among count, linear, and lognormal regression models

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JOURNAL OF INFORMETRICS 2015年第3期9卷 499-513页

作者： Ajiferuke, Isola Famoye, Felix Univ Western Ontario Fac Informat & Media Studies London ON N6A 5B7 Canada Cent Michigan Univ Dept Math Mt Pleasant MI 48859 USA

The purpose of the study is to compare the performance of count regression models to those of linear and lognormal regression models in modelling count response variables in informetric studies. Identified count response variables in informetric studies include the number of authors, the number of references, the number of views, the number of downloads, and the number of citations received by an article. Also of a count nature are the number of links from and to a website. Data were collected from the United States Patent and Trademark Office (***), an open access journal (***), Web of Science, and Maclean's magazine. The datasets were then used to compare the performance of linear and lognormal regression models with those of Poisson, negative binomial, and generalized Poisson regression models. It was found that due to overdispersion in most response variables, the negative binomial regression model often seems to be more appropriate for informetric datasets than the Poisson and generalized Poisson regression models. Also, the regression analyses showed that linear regression model predicted some negative values for five of the nine response variables modelled, and for all the response variables, it performed worse than both the negative binomial and lognormal regression models when either Akaike's Information Criterion (AIC) or Bayesian Information Criterion (BIC) was used as the measure of goodness of fit statistics. The negative binomial regression model performed significantly better than the lognormal regression model for four of the response variables while the lognormal regression model performed significantly better than the negative binomial regression model for two of the response variables but there was no significant difference in the performance of the two models for the remaining three response variables. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Count response variable linear regression model Count regression models Negative binomial regression model Lognormal regression model Informetric studies

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