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Online monitoring variance change in a linear regression model with long-memory errors

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2025年

作者： Niang, Maocuo Chen, Zhanshou Li, Fuxiao Qinghai Normal Univ Sch Math & Stat Xining Peoples R China State Key Lab Tibetan Intelligence Xining Peoples R China Xian Univ Technol Dept Appl Math Xian Peoples R China

This study extends the modified moving sum statistic (mMOSUM) method to online monitoring variance changes in a linear regression model with long-memory time series errors. Under the null hypothesis, the limit distribution is obtained by modifying the boundary function, and the consistency of the method is proved under the alternative hypothesis. The results of numerical simulation show that the mMOSUM method remains effective when the linear regression model has long-memory time series errors. As the location of the change point moves further back, the effect of the modified method on the increase of the power and the reduction of the run length is more obvious. Finally, we demonstrate the effectiveness of this method through a set of actual data.

关键词： linear regression model long-memory time series change point monitoring mMOSUM method

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linear regression model for noise pollution over central Delhi to highlight the alarming threat for the environment

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modelING EARTH SYSTEMS AND ENVIRONMENT 2023年第2期9卷 1909-1921页

作者： Dwivedi, Adwaita Kumar, Nishant Singh, Priyanka Chourey, Parag Kamra, Rohan Soni, Kirti Singh, Mahavir CSIR Natl Phys Lab Dr KS Krishnan Marg New Delhi India CSIR Adv Mat & Proc Res Bhopal Madhya Pradesh India Acad Sci & Innovat Res AcSIR Ghaziabad 201002 India

Noise pollution is the most ignored and underappreciated problem in the world. Even though scientists all over the world have done a lot of research on noise mapping and possible solutions, these solutions are still a long way from being put into practice. Noise reduction is an important step toward making a community that can last for a long time. Without systematic noise mapping, it is hard to figure out how noise changes in space and time. Using the Norsonic sound level meter, this research provides a novel methodological framework to integrate linear regression models with acoustic propagation for dynamic noise maps in Central Delhi. The 17 most sensitive receptors are also located in the study area. The noise mapping has been performed with the help of Dhwani pro and Arc-GIS software. The results from the noise mapping shows that the study area has noise at hazardous level. The second order linear regression noise prediction model has also been used for prediction of noise levels with taking parameters vehicle flow, % of heavy motor vehicle and light motor vehicle as inputs. The prediction performance is ascertained using the statistical test. The predicted noise values show good correlation with the observed noise levels i.e., R of 0.90. The isolation barriers of 5 m height are also introduced in the noise mapping analysis using Dhwani pro. These barriers represent substantial improvement in the noise level. The overall scenario of noise pollution in the study area is at alarming level and requires immediate planning to control the situation.

关键词： Arc-GIS Dhwani Pro linear regression model Noise modelling Noise pollution levels

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Identification of Parameters of a linear regression model by Simultaneous Optimization of Two Heterogeneous Criteria

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THEORETICAL FOUNDATIONS OF CHEMICAL ENGINEERING 2024年第3期58卷 905-908页

作者： Noskov, S. I. Ovsyannikov, I. V. Irkutsk State Transport Univ Irkutsk Russia

The article provides a brief overview of works related to the use of various criteria for the adequacy of mathematical models, each of which reflects certain characteristics in the form of a model description of the functioning of the process or object under study. In particular, the considered works deal with a finite mixed regression model, which forms sample clusters and jointly uses several mixed criteria simultaneously, ensures the selection of common functions among tasks and cluster components, allows working with anomalous tasks, and takes into account outliers in samples;the problem of constructing a heterogeneous ensemble of models, where three self-adapting genetic algorithms with different control parameters of mutation, crossing, and selection, adjusted during execution, are proposed;the problem of filling missing data in regression modeling, where 11 heterogeneous ensemble filling methods are proposed and constructed, the members of which are two, three, or four of the following single methods: K-nearest neighbors, expectation maximization, support vector regression, and decision trees;and a semiparametric modeling approach that combines parametric regression analysis and nonparametric analogical estimation. An algorithm is proposed for solving the problem of estimating unknown parameters using two criteria simultaneously: the minimum sum of the approximation error modules and the maximum consistency of behavior between the given and model-calculated values of the dependent variable in continuous form. This algorithm involves first identifying the Pareto vertices of a given polyhedron and then checking the Pareto property of the edges connecting their images in the criterion space. The computational problems that arise in this case are reduced to linear programming problems. A simple numerical example is solved.

关键词： linear regression model multicriteria parameter estimation least modulus method adequacy criteria behavior consistency Pareto set linear programming

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On the jackknife Kibria-Lukman estimator for the linear regression model

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2023年第12期52卷 6116-6128页

作者： Ugwuowo, Fidelis Ifeanyi Oranye, Henrietta Ebele Arum, Kingsley Chinedu Univ Nigeria Nsukka Dept Stat Nsukka Enugu State Nigeria

The linear regression model explores the relationship between the dependent variable and the independent variables. The ordinary least squared estimator (OLSE) is widely applicable to estimate the parameters of the model. However, OLSE suffered a breakdown when the independent variables are linearly dependent- a condition called multicollinearity. The Kibria-Lukman estimator (KLE) was suggested as an alternative to the OLSE and some other estimators (ridge and Liu estimators). In this paper, we developed a Jackknifed version of the Kibria-Lukman estimator- the estimator is named the Jackknifed KL estimator (JKLE). We derived the statistical properties of the new estimator and compared it theoretically with the KLE and some other existing estimators. Theoretically, the result revealed that JKLE possesses the lowest MSE when compared with the KLE and some other existing estimators. Finally, JKLE reduced the bias and the mean squared error (MSE) of KLE in both simulation and real-life analysis. JKLE dominates other methods considered in this study.

关键词： Jackknifed KL estimator linear regression model multicollinearity MSE OLS

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Bayesian empirical likelihood of linear regression model with current status data

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2023年第20期52卷 7323-7333页

作者： Liu, Binxia Zhao, Hui Wang, Chunjie Zhongnan Univ Econ & Law Coll Stat & Math Wuhan Peoples R China Changchun Univ Technol Coll Math & Stat Changchun 130012 Peoples R China

Empirical likelihood has been widely used in survival data analysis recently. In this paper, we combine Bayesian idea with empirical likelihood and develop a Bayesian empirical likelihood method to analyze current status data based on the linear regression model. By constructing unbiased transformation of current status data, we derive an empirical log-likelihood function. The normal prior distribution and a Metro-Hastings method are presented to make Bayesian posterior inference. The theoretical properties of the estimators are proposed. Extensive simulation studies indicate that Bayesian empirical likelihood method performs much better than the empirical likelihood method in terms of coverage probability. Finally, we apply two real data to illustrate the proposed method.

关键词： Current status data linear regression model Bayesian empirical likelihood MHadaptive package coverage probabilities

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Consistency of semi-parametric maximum likelihood estimator under identifiability conditions for the linear regression model with type I right censoring data

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2023年第22期52卷 8152-8168页

作者： Dong, Junyi St Ambrose Univ Math & Stat Dept Davenport IA 52803 USA

The consistency of the semi-parametric maximum likelihood estimator (SMLE) under the semi-parametric linear regression model with right-censoring data (SPLRRC model) has not been studied under the necessary and sufficient condition for the identifiability of the parameters. In this paper, we discuss the necessary and sufficient condition for the consistency of SMLE under type I right censoring.

关键词： linear regression model semi-parametric model semi-parametric MLE consistency

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Removing temperature drift for bee colony weight measurements based on linear regression model and Kalman filter

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BIOSYSTEMS ENGINEERING 2023年第1期233卷 1-20页

作者： Jia, Bowen Yang, Fangchao Zhao, Menghao Chu, Liangyu Chen, Bingxue Li, Honggang Li, Qingqing Zhang, Deng Li, Yunfan Lu, Chuanqi Lu, Yuntao Liu, Shengping Hong, Wei Huazhong Univ Sci & Technol PGMF Hubei Key Lab Gravitat & Quantum Phys MOE Key Lab Fundamental Phys Quant Measurement Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Sch Phys Wuhan 430074 Peoples R China Intelligent Comp Hardware Ctr Zhejiang Lab Hangzhou 311121 Peoples R China Huazhong Univ Sci & Technol Tongji Med Coll Sch Basic Med Wuhan 430074 Peoples R China Huazhong Agr Univ Coll Engn Wuhan 430070 Peoples R China Chinese Acad Agr Sci Minist Agr & Rural Affairs Agr Informat Inst Key Lab Agr Blockchain Applicat Beijing 100081 Peoples R China

In precision beekeeping, bee colony weight is an important indicator to monitor the behaviours such as foraging and swarming. However, ambient temperature variations can greatly affect the measured values. In this paper, a combined method with linear regression model and Kalman filter is proposed to reduce the influence of ambient temperature. Monitoring data is collected to validate the effectiveness of the proposed method. Moreover, methods that solely rely on the statistic model or Kalman filter are investigated as a comparison with the proposed method. The compensation results indicate that the proposed method outperforms the two others, and is feasible and effective in temperature drift removal. The mean absolute errors can be decreased over 40% from that before removal during periods of no honeycombs, the coefficient of variations can also be reduced by over 40% and 5% respectively during the periods of no bees and bees in the beehives. As the proposed method can improve the reading accuracy of bee colony weight, it has potential to benefit the precision beekeeping and basic research on bee activities.& COPY;2023 IAgrE. Published by Elsevier Ltd. All rights reserved.

关键词： bee colony weight temperature drift linear regression model Kalman filter precision beekeeping

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A nonlinear mixed-integer programming approach for variable selection in linear regression model

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2023年第11期52卷 5434-5445页

作者： Roozbeh, Mahdi Babaie-Kafaki, Saman Aminifard, Zohre Semnan Univ Fac Math Stat & Comp Sci POB 35195-363 Semnan Iran

Modern statistical studies often encounter regression models with high dimensions in which the number of features p is greater than the sample size n. Although the theory of linear models is well-established for the traditional assumption p < n, making valid statistical inference in high dimensional cases is a considerable challenge. With recent advances in technologies, the problem appears in many biological, medical, social, industrial, and economic studies. As known, the LASSO method is a popular technique for variable selection/estimation in high dimensional sparse linear models. Here, we show that the prediction performance of the LASSO method can be improved by eliminating the structured noises through a mixed-integer programming approach. As a result of our analysis, a modified variable selection/estimation scheme is proposed for a high dimensional regression model which can be considered as an alternative of the LASSO method. Some numerical experiments are made on the classical riboflavin production and some simulated data sets to shed light on the practical performance of the suggested method.

关键词： linear regression model LASSO method Mixed-integer programming Sparsity Variable selection

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Condition-index based new ridge regression estimator for linear regression model with multicollinearity

KUWAIT JOURNAL OF SCIENCE

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KUWAIT JOURNAL OF SCIENCE 2023年第2期50卷 91-96页

作者： Dar, Irum Sajjad Chand, Sohail Shabbir, Maha Kibria, B. M. Golam Univ Punjab Coll Stat & Actuarial Sci Lahore Pakistan Florida Int Univ Dept Math & Stat Miami FL USA

Ridge regression is employed to estimate the regression parameters while circumventing the multicollinearity among independent variables. The ridge parameter plays a vital role as it controls bias-variance tradeoff. Several methods for choosing the ridge parameter are suggested in the literature. In this paper, we suggest a new ridge estimator which is a function of condition index, number of predictors and error variance. This new proposal has the novelty to have a sort of automatic dealing with the multicollinearity level and signal-to-noise ratio. Extensive Monte Carlo simulations are performed to evaluate the performance of the proposed ridge regression estimators in various scenarios. It has been shown that the our proposed estimator outperforms the closely related estimators in terms of minimum mean squared error (MSE). Finally, two real life applications are also provided.

关键词： Condition index linear regression model MSE Multicollinearity Monte Carlo simulation Ridge regression

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On Some Robust Liu Estimators for the linear regression model with Outliers: Theory, Simulation and Application

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JOURNAL OF STATISTICAL THEORY AND PRACTICE 2024年第4期18卷 1-32页

作者： Ahmad, Shakeel Majid, Abdul Aslam, Muhammad Bahauddin Zakariya Univ Dept Stat Multan Pakistan Pakistan Bur Stat Reg Off Multan Pakistan

The Liu estimator (LE) is a widely used estimation method for multiple linear regression model to combat the problem of multicollinearity. The LE is sensitive to the presence of outliers in y-direction. To tackle the simultaneous issue of multicollinearity and outlier in the multiple linear regression model, the Liu M-estimator (LME) is proposed in the literature. The selection of proper estimator for Liu parameter d is very crucial when using the LE as well as for the case of LME. However, this issue has not gained much attention of the researchers in the case of LME. This study proposes some robust estimators of d based on robust estimates for the case of LME. The performance of proposed estimators is compared with the available estimators of d using the Monte Carlo simulations and a real application where the mean squared error is considered as a performance evaluation criterion. Results show a superb performance of the proposed robust estimators as compared to the LE, ordinary least squares and M-estimation methods.

关键词： linear regression model Liu estimator Liu M-estimator M-estimator Multicollinearity Outlier C20 C25

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