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Parallel maximum likelihood estimator for multiple linear regression models

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2015年 273卷 251-263页

作者： Guo, Guangbao You, Wenjie Qian, Guoqi Shao, Wei Shandong Univ Technol Dept Stat Zibo 255000 Peoples R China Shandong Univ Sch Math Jinan 250100 Peoples R China Xiamen Univ Dept Automat Xiamen 361005 Peoples R China Univ Melbourne Dept Math & Stat Parkville Vic 3010 Australia Qufu Normal Univ Sch Management Rizhao 276800 Peoples R China

Consistency and run-time are important questions in performing multiple linear regression models. In response, we introduce a new parallel maximum likelihood estimator for multiple linear models. We first provide an equivalent condition between the method and the generalized least squares estimator. We also consider the rank of projections and the eigenvalue. We then present consistency when a stable solution exists. In this paper, we describe several consistency theorems and perform experiments on consistency, outlier, and scalability. Finally, we fit the proposed method onto bankruptcy data. (C) 2014 Elsevier B.V. All rights reserved.

关键词： multiple linear regression models Parallel computing Maximum likelihood estimator Consistency Outlier

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Updated multiple linear regression models for Predicting Chronic Aluminum Toxicity to Freshwater Aquatic Organisms and Developing Water Quality Guidelines

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ENVIRONMENTAL TOXICOLOGY AND CHEMISTRY 2020年第9期39卷 1724-1736页

作者： DeForest, David K. Brix, Kevin, V Tear, Lucinda M. Cardwell, Allison S. Stubblefield, William A. Nordheim, Eirik Adams, William J. Windward Environm Seattle WA 98119 USA EcoTox Miami FL USA Oregon State Univ Corvallis OR 97331 USA European Aluminium Brussels Belgium Red Cap Consulting Lake Point UT USA

multiple linear regression (MLR) models for predicting chronic aluminum toxicity to a cladoceran (Ceriodaphnia dubia) and a fish (Pimephales promelas) as a function of 3 toxicity-modifying factors (TMFs)-dissolved organic carbon (DOC), pH, and hardness-have been published previously. However, the range over which data for these TMFs were available was somewhat limited. To address this limitation, additional chronic toxicity tests with these species were subsequently conducted to expand the DOC range up to 12 mg/L, the pH range up to 8.7, and the hardness range up to 428 mg/L. The additional toxicity data were used to update the chronic MLR models. The adjustedR(2)for theC. dubia20% effect concentration (EC20) model increased from 0.71 to 0.92 with the additional toxicity data, and the predictedR(2)increased from 0.57 to 0.89. ForP. promelas, the adjustedR(2)increased from 0.87 to 0.92 and the predictedR(2)increased from 0.72 to 0.87. The high predictedR(2)relative to the adjustedR(2)indicates that the models for both species are not overly parameterized. When data forC. dubiaandP. promelaswere pooled, the adjustedR(2)values were comparable to the species-specific models (0.90 and 0.88 forC. dubiaandP. promelas, respectively). This indicates that chronic aluminum EC20s forC. dubiaandP. promelasrespond similarly to variation in DOC, pH, and hardness. Overall, the pooled model predicted EC20s that were within a factor of 2 of observed in 100% of theC. dubiatests and 94% of theP. *** Toxicol Chem2020;00:1-13. (c) 2020 SETAC

关键词： Aluminum Bioavailability multiple linear regression models Water quality guidelines

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Upper and Lower Bound Interval Forecasting Methodology Based on Ideal Boundary and multiple linear regression models

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WATER RESOURCES MANAGEMENT 2019年第3期33卷 1203-1215页

作者： Li, Wei Zhou, Jianzhong Chen, Lu Feng, Kuaile Zhang, Hairong Meng, Changqing Sun, Na Chongqing Water Resources & Elect Engn Coll Chongqing 402160 Peoples R China Huazhong Univ Sci & Technol Sch Hydropower & Informat Engn Wuhan 430074 Hubei Peoples R China Hubei Key Lab Digital Valley Sci & Technol Wuhan 430074 Hubei Peoples R China

The uncertainty research of hydrological forecast attracts the attention of a host of hydrological experts. Prediction Interval (PI) is a convinced method that can ensure the forecasting accuracy meanwhile take uncertainty range into consideration. While the existed Prediction Interval methods need algorithm optimization and are susceptible to local optima, so it is particularly urgent to provide an efficient Prediction Interval (PI) model with excellent performance. This paper proposes a novel upper and lower bound interval estimation model to rapidly define the PI and reduce the amount of calculation to implement convenient and high precise hydrological forecast. Above all, the ideal upper and lower bounds are defined according to the relative width or absolute width. Then, the proposed model is utilized to forecast interval runoff via least square method and multiple linear regression methods. The estimated interval inclusion ratio, interval width, symmetry, and root-mean-square error which are popular used to judge the precision serve as accuracy evaluation indexes. The measured discharge data from five hydrological stations which located upstream of the Yangtze River is applied for interval forecasting. Compared with the results of neural network-based upper and lower bound interval estimation model, the proposed method yields higher forecasting accuracy, meanwhile, the ideal upper and lower bounds successfully minimize the number of processes which require a mass of parameter searching and optimization.

关键词： Interval hydrological forecasting The ideal boundary multiple linear regression models Upper and lower bound estimation

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Air Pollution Monitoring Using Cost-Effective Devices Enhanced by Machine Learning

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SENSORS 2025年第5期25卷 1423-1423页

作者： Colleaux, Yanis Willaume, Cedric Mohandes, Bijan Nebel, Jean-Christophe Rahman, Farzana Natl Sch Stat & Data Anal ENSAI Blaise Pascal BP37203 F-35172 Bruz France Natl Grad Sch Engn Caen ENSICAEN 6 Blvd Marechal Juin14050 Caen F-CS45053 Caen France Technocomm Consulting Ltd The Barn Long Lane Newbury RG14 2TB England Kingston Univ Fac Engn Comp & Environm Holmwood HouseGrove Crescent Kingston Upon Thames KT1 2EE England

Given the significant impact of air pollution on global health, the continuous and precise monitoring of air quality in all populated environments is crucial. Unfortunately, even in the most developed economies, current air quality monitoring networks are largely inadequate. The high cost of monitoring stations has been identified as a key barrier to widespread coverage, making cost-effective air quality monitoring devices a potential game changer. However, the accuracy of the measurements obtained from low-cost sensors is affected by many factors, including gas cross-sensitivity, environmental conditions, and production inconsistencies. Fortunately, machine learning models can capture complex interdependent relationships in sensor responses and thus can enhance their readings and sensor accuracy. After gathering measurements from cost-effective air pollution monitoring devices placed alongside a reference station, the data were used to train such models. Assessments of their performance showed that models tailored to individual sensor units greatly improved measurement accuracy, boosting their correlation with reference-grade instruments by up to 10%. Nonetheless, this research also revealed that inconsistencies in the performance of similar sensor units can prevent the creation of a unified correction model for a given sensor type.

关键词： air pollution monitoring low-cost sensors electrochemical sensors non-dispersive infrared sensors sensor performance variability measurement correction sensor calibration data-driven correction machine learning multiple linear regression models

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Conservative sample size for multiple regression models

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2023年第15期52卷 5527-5533页

作者： McIntosh, Matthew J. Experis Clin Solut Stat St Louis MO 63141 USA

A lower bound is given for the multiple correlation coefficient R. This lower bound is used to obtain conservative sample sizes for testing the hypothesis H-0: R-2 = 0 vs H-1: R-2 > 0 which is one method for obtaining the sample size for a multiple linear regression Model. Results are given which can be used to determine how close the conservative sample sizes are to those obtained using the true value of R.

关键词： multiple linear regression models sample size multiple correlation coefficient

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Impact of Variable Transformations on multiple regression models for Enhancing Gait Normalization 23

Impact of Variable Transformations on Multiple Regression Mo...

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6th International Conference on Mathematics and Statistics, ICoMS 2023

作者： Ferreira, Flora Barrios, Jhonathan Barbosa, Paulo Gago, Miguel F Bicho, Estela Erlhagen, Wolfram Centre of Mathematics School of Sciences University of Minho Portugal University of Minho Portugal Algoritmi Research Centre School of Engineering University of Minho Portugal

ISBN: (纸本)9798400700187

Gait analysis has become an important tool in clinical practice for monitoring disease progression and evaluating therapeutic interventions. However, a subject's gait characteristics can be affected by physical characteristics such as age and height, which can interfere with accurate comparisons between subjects. MLR normalization has been shown to be effective in reducing interference from subject-specific physical properties, but non-linear effects can still impact the results. In this study, the independent variables were transformed to improve normalization performance, and the results indicate that using MR normalization with data transformation can effectively de-correlate physical characteristics from gait variables, improving the model fit and augment the capability to compare subjects with varying physical characteristics. This study provides valuable insights into the use of MLR models for gait normalization, with potential applications in clinical practice and research. © 2023 Owner/Author.

关键词： Data transformation Gait analysis Gait normalization multiple linear regression models

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Development of a Powerful Data-Analysis Tool Using Nonparametric Smoothing models To Identify Drillsites in Tight Shale Reservoirs With High Economic Potential

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SPE JOURNAL 2018年第3期23卷 719-736页

作者： Cai, Quan Yu, Wei Liang, Hwa Chi Liang, Jenn-Tai Wang, Suojin Wu, Kan Texas A&M Univ Dept Stat College Stn TX 77843 USA Texas A&M Univ Harold Vance Dept Petr Engn College Stn TX 77843 USA Texas A&M Univ Stat & Epidemiol & Biostat College Stn TX 77843 USA

The oil-and-gas industry is entering an era of "big data" because of the huge number of wells drilled with the rapid development of unconventional oil-and-gas reservoirs during the past decade. The massive amount of data generated presents a great opportunity for the industry to use data-analysis tools to help make informed decisions. The main challenge is the lack of the application of effective and efficient data-analysis tools to analyze and extract useful information for the decision-making process from the enormous amount of data available. In developing tight shale reservoirs, it is critical to have an optimal drilling strategy, thereby minimizing the risk of drilling in areas that would result in low-yield wells. The objective of this study is to develop an effective data-analysis tool capable of dealing with big and complicated data sets to identify hot zones in tight shale reservoirs with the potential to yield highly productive wells. The proposed tool is developed on the basis of nonparametric smoothing models, which are superior to the traditional multiplelinear-regression (MLR) models in both the predictive power and the ability to deal with nonlinear, higher-order variable interactions. This data-analysis tool is capable of handling one response variable and multiple predictor variables. To validate our tool, we used two real data sets-one with 249 tight oil horizontal wells from the Middle Bakken and the other with 2,064 shale gas horizontal wells from the Marcellus Shale. Results from the two case studies revealed that our tool not only can achieve much better predictive power than the traditional MLR models on identifying hot zones in the tight shale reservoirs but also can provide guidance on developing the optimal drilling and completion strategies (e.g., well length and depth, amount of proppant and water injected). By comparing results from the two data sets, we found that our tool can achieve model performance with the big data set (2,064 Marce

关键词： Data analysis Big data Nonparametric Smoothing models Unconventional oil and gas reservoirs multiple linear regression models

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Modelling of haloacetic acid concentrations in a United Kingdom drinking water system

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JOURNAL OF WATER SUPPLY RESEARCH AND TECHNOLOGY-AQUA 2011年第5期60卷 275-285页

作者： Zhang, Yanping Martinez, David Collins, Christopher Graham, Nigel Templeton, Michael R. Huang, Jin Nieuwenhuijsen, Mark Univ London Imperial Coll Sci Technol & Med Dept Civil & Environm Engn London SW7 2AZ England Univ Reading Dept Soil Sci Reading RG6 6DW Berks England Ctr Res Environm Epidemiol CREAL Barcelona 08003 Spain IMIM Barcelona 08003 Spain CIBERESP Barcelona 08003 Spain

Haloacetic acids (HAAs) are formed during the chlorination of water containing organic matter but predictive models for their formation are not well established at present and have not been applied to UK water systems. In this paper two different modelling approaches have been applied and evaluated to a selected UK drinking water system. The first approach involved the development of statistical predictive models for the HAA formation by using multiple linear regression with appropriate water quality and operational parameters obtained from sampling, and the second approach employed the simulated distribution system (SDS) test. Statistically significant predictors were trihalomethane (THM) levels, pH, temperature, total chlorine total organic carbon, UV254, bromide concentration and residence time, but the importance of each varied with HAA species. The models that generally explained most of the variance of individual and total HAAs included THMs as a predictor variable. The use of the SDS-HAA test included quantification of individual HAA species. The concentration of total HAA and individual compounds in the SDS test and field samples were comparable immediately after chlorination, but with increasing residence time the concentration of HAAs in the selected water distribution system were greater than those found in the SDS test.

关键词： disinfection by-products distribution system drinking water haloacetic acids multiple linear regression models

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Correlation of Particulate Matter with Airborne Fungi in Schools in Greece

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INTERNATIONAL JOURNAL OF VENTILATION 2013年第1期12卷 1-15页

作者： Dorizas, P. V. Kapsanaki-Gotsi, E. Assimakopoulos, M. N. Santamouris, M. Univ Athens Fac Phys Dept Environm Phys & Meteorol GR-15784 Athens Greece Univ Athens Fac Biol Dept Systemat & Ecol GR-15784 Athens Greece

The concentration levels of particulate matter (PM), airborne fungi, carbon dioxide as well as temperature and relative humidity were investigated in the indoor and outdoor environment of two schools in Athens, Greece during the period January to May 2011. The overall concentration ranges of the indoor measured pollutants were: PM10: 14.92-166.18 mu g/m(3), PM2.5: 3.16-31.27 mu g/m(3), PM1: 0.72-9.01 mu g/m(3), UFP: 4188-63093 pt/cm(3), total airborne fungi: 28-2098 CFU/m(3) and CO2: 389-1717 ppm. The relationships between PM and airborne fungi were mainly examined, and bivariate correlations of all the measured environmental parameters are also reported. The results indicate that PM of certain aerodynamic diameters significantly correlate to the total airborne fungi and their prevalent genera, Penicillium, Cladosporium and Aspergillus. Principal Component Analysis (PCA) was conducted so as to cluster variables of common characteristics. Furthermore, simple and multiple linear regression models were developed to investigate several cases of dependent variables to be used for prediction purposes in health risk assessments.

关键词： indoor air quality schools particulate matter airborne fungi PCA multiple linear regression models

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Rapid changes in the seasonal sea level cycle along the US Gulf coast from the late 20th century

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GEOPHYSICAL RESEARCH LETTERS 2014年第2期41卷 491-498页

作者： Wahl, Thomas Calafat, Francisco M. Luther, Mark E. Univ S Florida Coll Marine Sci St Petersburg FL 33701 USA Univ Siegen Res Ctr Siegen FoKoS D-57068 Siegen Germany Natl Oceanog Ctr Southampton Hants England

Temporal variations of the seasonal sea level harmonics throughout the 20(th) and early 21(st) century along the United States Gulf coast are investigated. A significant amplification of the annual sea level cycle from the 1990s onward is found, with both lower winter and higher summer sea levels in the eastern Gulf. Ancillary data are used to build a set of multiple regression models to explore the mechanisms driving the decadal variability and recent increase in the annual cycle. The results suggest that changes in the air surface temperature toward warmer summers and colder winters and changes in mean sea level pressure explain most of the amplitude increase. The changes in the seasonal sea level cycle are shown to have almost doubled the risk of hurricane induced flooding associated with sea level rise since the 1990s for the eastern and north-eastern Gulf of Mexico coastlines. Key Points

Seasonal sea level changes in the Gulf of Mexico are investigated A significant increase in the annual amplitude is found for the recent past Seasonal changes have exacerbated the flood risk in the eastern Gulf

关键词： Gulf of Mexico coastal seasonal sea level tide gauge data atmospheric reanalysis multiple linear regression models flood risk

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