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EMPIRICAL　BAYES　ESTIMATION　FOR　ESTIMABLE　FUNCTION　OF　regression　COEFFICIENT　IN　A　MULTIPLE　linear　regression　model

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Acta Mathematica Scientia 1996年第S1期16卷 22-33页

作者：韦来生 University of Science and Technology of China Hefei 230026 China

In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.

关键词： linear regression model estimable function empirical Bayes estimation convergence rates

Changes of coastline and tidal flat and its implication for ecological protection under human activities: Take China’s Bohai Bay as an example

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China Geology 2024年第1期7卷 26-35页

作者： Yong Li Ming-zheng Wen Heng Yu Peng Yang Fei-cui Wang Fu Wang Tianjin Center China Geological SurveyMinistry of Natural ResourcesTianjin 300170China Key Laboratory of Coast Geo-environment China Geological SurveyMinistry of Natural ResourcesTianjin 300170China Tianjin Key Laboratory of Coast Geological Processes and Environmental Safety Tianjin 300170China Hebei University of Environmental Engineering Qinhuangdao 066102China Hebei Engineering Research Center for Ecological Restoration of seaward Rivers and Coastal Waters Qinhuangdao 066102China Department of Earth and Environment Boston UniversityBoston 02215USA

The change processes and trends of shoreline and tidal flat forced by human activities are essential issues for the sustainability of coastal area,which is also of great significance for understanding coastal ecological environment changes and even global changes.Based on field measurements,combined with linear regression(LR)model and Inverse Distance Weighing(IDW)method,this paper presents detailed analysis on the change history and trend of the shoreline and tidal flat in Bohai Bay.The shoreline faces a high erosion chance under the action of natural factors,while the tidal flat faces a different erosion and deposition patterns in Bohai Bay due to the impact of human activities.The implication of change rule for ecological protection and recovery is also discussed.Measures should be taken to protect the coastal ecological environment.The models used in this paper show a high correlation coefficient between observed and modeling data,which means that this method can be used to predict the changing trend of shoreline and tidal flat.The research results of present study can provide scientific supports for future coastal protection and management.

关键词： Shoreline Tidal flat Erosion deposition patterns Changing trend Ecological protection Human activity linear regression model Inverse distance weighing method Prediction Bohai Bay

Sequential Monitoring Variance Change in linear regression model

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Journal of Mathematical Research and Exposition 2010年第4期30卷 610-618页

作者： Zhan Shou CHEN Zheng TIAN Rui Bing QIN Cheng Cai LENG1 Department of Applied Mathematics Northwestern Polytechnical University Shaanxi 710129 P. R. China State Key Laboratory of Remote Sensing Science Institute of Remote Sensing Applications Chinese Academy of Sciences Beijing 100101 P. R. China

The paper investigates the sequential observations’ variance change in linear regression model. The procedure is based on a detection function constructed by residual squares of CUSUM and a boundary function which is designed so that the test has a small probability of false alarm and asymptotic power one. Simulation results show our monitoring procedure performs well when variance change occurs shortly after the monitoring time. The method is still feasible for regression coefficients change or both variance and regression coefficients change problem.

关键词： sequential monitoring variance change linear regression model residuals.

A Study of EM Algorithm as an Imputation Method: A model-Based Simulation Study with Application to a Synthetic Compositional Data

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Open Journal of modelling and Simulation 2024年第2期12卷 33-42页

作者： Yisa Adeniyi Abolade Yichuan Zhao Department of Mathematics and Statistics Georgia State University Atlanta Georgia USA

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

关键词： Compositional Data linear regression model Least Square Method Robust Least Square Method Synthetic Data Aitchison Distance Maximum Likelihood Estimation Expectation-Maximization Algorithm k-Nearest Neighbor and Mean imputation

Variable Selection in Logistic regression model

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Chinese Journal of Electronics 2015年第4期24卷 813-817页

作者： ZHANG Shangli ZHANG Lili QIU Kuanmin LU Ying CAI Baigen School of Science Beijing Jiaotong University State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong University Department of Statistic Chonnam National University

Variable selection is one of the most important problems in pattern recognition. In linear regression model, there are many methods can solve this problem,such as Least absolute shrinkage and selection operator(LASSO) and many improved LASSO methods, but there are few variable selection methods in generalized linear models. We study the variable selection problem in logistic regression model. We propose a new variable selection method – the logistic elastic net, prove that it has grouping effect which means that the strongly correlated predictors tend to be in or out of the model together. The logistic elastic net is particularly useful when the number of predictors(p) is much bigger than the number of observations(n). By contrast, the LASSO is not a very satisfactory variable selection method in the case when p is more larger than n. The advantage and effectiveness of this method are demonstrated by real leukemia data and a simulation study.

关键词： Variable selection LASSO linear regression model Logistic elastic net Logistic regression model

Predictor Variables Influencing Visibility Prediction Based on Elevation and Its Range for Improving Traffic Operations and Safety

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Journal of Transportation Technologies 2022年第3期12卷 439-452页

作者： Ajinkya Sadashiv Mane Srinivas Subrahmanyam Pulugurtha Venkata Ramana Duddu Christopher Michael Godfrey IDEAS Center Civil & Environmental Engineering Department The University of North Carolina at Charlotte Charlotte USA Atmospheric Sciences Department The University of North Carolina at Asheville Asheville USA

Low visibility condition hinders both air traffic and road traffic operations. Accurate forecasting of visibility condition helps aircraft operators and travelers to make better decisions and improve their safety. It is, therefore, essential to investigate and identify the predictor variables that could influence and help predict visibility. The objective of this study is to identify the predictor variables that influence visibility. Four years of surface weather observations, from January 2011 to December 2014, were collected from the weather stations located in and around the state of North Carolina, USA for the model development. Ordinary least squares (OLS) and weighted least squares (WLS) regression models were developed for different visibility and elevation ranges. The results indicate that elevation, cloud cover, and precipitation are negatively associated with the visibility in visibility less than 15,000 m model. The elevation, cloud cover and the presence of water bodies within the vicinity play an important role in the visibility less than 2000 m model. The chances of low visibility condition are higher between six to twelve hours after the rainfall when compared to the first six hours after the rainfall. The results from this study help to understand the influence of predictor variables that should be dealt with to improve the traffic operations and safety concerning the visibility near the airports/road transportation network.

关键词： Visibility Prediction Weather Station linear regression model Elevation

Pause or No Pause?—Prosodic Phrase Boundaries Revisited

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Tsinghua Science and Technology 2008年第4期13卷 500-509页

作者：郑秋豫张俊祥 Phonetics Lab Institute of Linguistics Academia Sinica Taipei 11529

This study presents evidence from analyses of the acoustic parameters of fluent continuous speech to show that within-paragraph prosodic phrase boundaries are related more to contrasts of neighborhood prosodic states rather than between-phrase pause durations; prosodic states receive more constraints from higher level discourse information. By revising a modular acoustic model by Tseng＇s hierarchical prosodic phrase grouping framework and examining the much varied prosodic phrase （PPh） boundary B3 within speech paragraph, we show that statistical accounts of layered contributions reveal distinct contrasts between boundary immediate duration and intensity patterns irrespective of pause duration. Contrasts of FO contour patterns were also observed in these locations. Evidence was also obtained to illustrate how PPh boundary states are specified more by higher level discourse information than by lower level prosodic word construction. These combined results suggest that contrastive neighboring prosodic states are more significant cues to PPh boundaries than boundary pause duration. The results also help explain why in fluent speech between-phrase pause durations vary greatly, and can be applied to automatic speech segmentation.

关键词： fluent speech prosody hierarchical prosody group prosodic state prosodic phrase boundary break discourse prosody linear regression model

Google timeline accuracy assessment and error prediction

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Forensic Sciences Research 2018年第3期3卷 240-255页

作者： Andrea Macarulla Rodriguez Christian Tiberius Roel van Bree Zeno Geradts Netherlands Forensic Institute Den HaagThe Netherlands Delft University of Technology DelftThe Netherlands

Google Location Timeline,once activated,allows to track devices and save their locations.This feature might be useful in the future as available data for evidence in investigations.For that,the court would be interested in the reliability of these data.The position is presented in the form of a pair of coordinates and a radius,hence the estimated area for tracked device is enclosed by a circle.This research focuses on the assessment of the accuracy of the locations given by Google Location History Timeline,which variables affect this accuracy and the initial steps to develop a linear multivariate model that can potentially predict the actual error with respect to the true location considering environmental variables.The determination of the potential influential variables(configuration of mobile device connectivity,speed of movement and environment)was set through a series of experiments in which the true position of the device was recorded with a reference Global Positioning System(GPS)device with a superior order of accuracy.The accuracy was assessed measuring the distance between the Google provided position and the de facto one,later referred to as Google error.If this Google error distance is less than the radius provided,we define it as a hit.The configuration that has the largest hit rate is when the mobile device has GPS available,with a 52%success.Then the use of 3G and 2G connection go with 38%and 33%respectively.The Wi-Fi connection only has a hit rate of 7%.Regarding the means of transport,when the connection is 2G or 3G,the worst results are in Still with a hit rate of 9%and the best in Car with 57%.Regarding the prediction model,the distances and angles from the position of the device to the three nearest cell towers,and the categorical(nonnumerical)variables of Environment and means of transport were taking as input variables in this initial study.To evaluate the usability of a model,a model hit is defined when the actual observation is within the 95%confidence interval provided by the model.Out of

关键词： Forensic science accuracy error Google Timeline linear regression model smartphone location

Predictive modelling of COVID-19 confirmed cases in Nigeria

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Infectious Disease modelling 2020年第1期5卷 543-548页

作者： Roseline O.Ogundokun Adewale F.Lukman Golam B.M.Kibria Joseph B.Awotunde Benedita B.Aladeitan Department of Computer Science Landmark University Omu AranNigeria Department of Physical Sciences Landmark University Omu AranNigeria Department of Mathematics and Statistics Florida International UniversityFloridaUSA Department of Computer Science University of IlorinIlorinNigeria

The coronavirus outbreak is the most notable world crisis since the SecondWorldWar.The pandemic that originated from Wuhan,China in late 2019 has affected all the nations of the world and triggered a global economic crisis whose impact will be felt for years to come.This necessitates the need to monitor and predict COVID-19 prevalence for adequate control.The linear regression models are prominent tools in predicting the impact of certain factors on COVID-19 outbreak and taking the necessary measures to respond to this crisis.The data was extracted from the NCDC website and spanned from March 31,2020 to May 29,2020.In this study,we adopted the ordinary least squares estimator to measure the impact of travelling history and contacts on the spread of COVID-19 in Nigeria and made a prediction.The model was conducted before and after travel restriction was enforced by the Federal government of Nigeria.The fitted model fitted well to the dataset and was free of any violation based on the diagnostic checks conducted.The results show that the government made a right decision in enforcing travelling restriction because we observed that travelling history and contacts made increases the chances of people being infected with COVID-19 by 85%and 88%respectively.This prediction of COVID-19 shows that the government should ensure that most travelling agency should have better precautions and preparations in place before re-opening.

关键词： COVID-19 Pandemic linear regression model Prediction Ordinary least squares estimator Diagnostic checks