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Simultaneous Model Change Detection in multivariate linear regression With Application to Indonesian Economic Growth Data

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JOURNAL OF APPLIED MATHEMATICS 2024年第1期2024卷 4499481-4499481页

作者： Somayasa, Wayan Djafar, Muhammad Kabil Muhtar, Norma Sutiari, Desak Ketut Halu Oleo Univ Fac Agr Dept Agrotechnol Kampus Anduonohu JL HEA Mokodompit Kendari 93232 Indonesia Mandala Waluya Univ Dept Med Elect Engn Kendari 93232 Anduonohu Indonesia

In this paper, we study asymptotic model change detection in multivariate linear regression by using the Kolmogorov-Smirnov function of the partial sum process of recursive residuals. We approximate the rejection region and also the power function of the test by establishing a functional central limit theorem for the sequence of the partial sum processes of the recursive residuals of the observations. When the assumed model is true, the limit process is given by the standard multivariate Brownian motion which does not depend on the regression functions. However, when the assumed model is not true (some models change), the limit process is represented by a vector of deterministic trend plus the standard multivariate Brownian motion. The finite sample size rejection region and the power of the test are investigated by means of Monte Carlo simulation. The simulation study shows evidence that the proposed test is consistent in the sense that it attains the power larger than the size of the test when the hypothesis is not true. We also demonstrate the application of the proposed test method to Indonesian economic growth data in which we test the adequacy of three-variate low-order polynomial model. The test result shows that the growth of the Indonesian economy is neither simultaneously constant nor linear. The test has successfully detect the appearance of a change in the model which is mainly caused by the COVID-19 pandemic in 2020.

关键词： economic growth functional central limit theorem gross domestic product Kolmogorov-Smirnov type test model change detection multivariate linear regression multivariate standard Brownian motion partial sum process recursive residuals

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Consistent Bayesian information criterion based on a mixture prior for possibly high-dimensional multivariate linear regression models

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SCANDINAVIAN JOURNAL OF STATISTICS 2023年第3期50卷 1022-1047页

作者： Kono, Haruki Kubokawa, Tatsuya MIT Dept Econ Cambridge MA 02139 USA Univ Tokyo Dept Econ Tokyo Japan

In the problem of selecting variables in a multivariate linear regression model, we derive new Bayesian information criteria based on a prior mixing a smooth distribution and a delta distribution. Each of them can be interpreted as a fusion of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Inheriting their asymptotic properties, our information criteria are consistent in variable selection in both the large-sample and the high-dimensional asymptotic frameworks. In numerical simulations, variable selection methods based on our information criteria choose the true set of variables with high probability in most cases.

关键词： consistency high-dimensional data information criterion mixture distribution multivariate linear regression variable selection

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Simultaneous confidence tubes for comparing several multivariate linear regression models

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BIOMETRICAL JOURNAL 2022年第2期64卷 290-300页

作者： Peng, Jianan Liu, Wei Bretz, Frank Hayter, A. J. Acadia Univ Dept Math & Stat Wolfville NS B4P 2R6 Canada Univ Southampton S3RI Southampton Hants England Univ Southampton Sch Math Southampton Hants England Novartis Pharmaceut Basel AG Switzerland Univ Denver Dept Stat & Operat Technol Denver CO USA

Much of the research on multiple comparison and simultaneous inference in the past 60 years or so has been for the comparisons of several population means. Spurrier seems to have been the first to investigate multiple comparisons of several simple linear regression lines using simultaneous confidence bands. In this paper, we extend the work of Liu et al. for finite comparisons of several univariate linear regression models using simultaneous confidence bands to finite comparisons of several multivariate linear regression models using simultaneous confidence tubes. We show how simultaneous confidence tubes can be constructed to allow more informative inferences for the comparison of several multivariate linear regression models than the current approach of hypotheses testing. The methods are illustrated with examples.

关键词： multiple comparisons multivariate linear regression simultaneous confidence bands simultaneous inference statistical simulation

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Predicting Daily Rainfall Amount Using Random Forest, multivariate linear regression, and Extreme Gradient Boosting 10

Predicting Daily Rainfall Amount Using Random Forest, Multiv...

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10th International Conference on Signal Processing and Communication, ICSC 2025

作者： Kumar, Barun Kumari, Punam Kumar, Ajit Prasad, Sanjeev Kumar School of Computer Science and Engineering Galgotias University Greater Noida India

ISBN: (纸本)9798331511890

To utilize water resources optimally, plan agricultural activities properly, and manage the risks of natural disasters in a country such as India where the economy relies heavily on the monsoon rains, accurate rainfall prediction on a day-to-day basis becomes very crucial. This work considers rainfall prediction of several regions in India and conduct a comparative evaluation of three machine learning models - multivariate linear regression, Random Forest, and Extreme Gradient Boosting. The models were built and validated based on a rich database that contained meteorological variables that correlate with rainfall. The effectiveness of these models was assessed concerning Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). It is evident from our results that the predictive capabilities of any of the models are good, however, the XGBoost model seems to shine out as the best since it had the least RMSE and MAE values even when compared to Random Forest and multivariate linear regression that were quite close. This performance hierarchy indicates that such performance of XGBoost may be a result of its potential of modeling complex non-linear relationships among the variables making it appropriate for the intricate task of predicting rainfall. The results show the prospects for further improvement in rainfall prediction with the application of more sophisticated machine learning approaches, which can noticeably integrate the complex relations between the obtained data and impacts on rainfall. © 2025 IEEE.

关键词： Model Optimization multivariate linear regression Rainfall Prediction Random Forest XGBoost

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Censored multivariate linear regression Model 25th

Censored Multivariate Linear Regression Model

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25th Congress of the Portuguese-Statistical-Society (SPE)

作者： Sousa, Rodney Pereira, Isabel Silva, Maria Eduarda Univ Aveiro Ctr Res & Dev Math & Applicat Aveiro Portugal Univ Porto Ctr Res & Dev Math & Applicat Porto Portugal

ISBN: (纸本)9783031127687;9783031127663;9783031127656

Often, real-life problems require modelling several response variables together. This work analyses a multivariate linear regression model when the data are censored. Censoring distorts the correlation structure of the underlying variables and increases the bias of the usual estimators. Thus, we propose three methods to deal with multivariate data under left censoring, namely Expectation Maximization (EM), DataAugmentation (DA) and Gibbs Sampler with Data Augmentation (GDA). Results from a simulation study showthat both DA and GDA estimates are consistent for low and moderate correlation. Under high correlation scenarios, EM estimates present a lower bias.

关键词： Censored data multivariate linear regression

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A multivariate linear regression Approach to Predict Ethene/1-Olefin Copolymerization Statistics Promoted by Group 4 Catalysts

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ACS CATALYSIS 2021年第7期11卷 4061-4070页

作者： Maity, Bholanath Cao, Zhen Kumawat, Jugal Gupta, Virendrakumar Cavallo, Luigi King Abdullah Univ Sci & Technol KAUST Catalysis Ctr KCC Thuwal 239556900 Saudi Arabia Reliance Ind Ltd Reliance Res & Dev Ctr Reliance Corp Pk Navi Mumbai 400701 India

We report a combined multivariate linear regression (MLR) and density functional theory (DFT) approach for predicting the comonomer incorporation rate in the copolymerization of ethene with 1olefins. The MLR model was trained to correlate the incorporation rate of a set of 19 experimental group 4 catalysts to steric and electronic features of the dichloride catalyst precursors. Although the assembled experimental data were produced in different laboratories and both propene and 1hexene copolymerization results were considered, the trained MLR model results in a R-2 value of 0.82 and a leave-one-out Q(2) value of 0.72. The trained model was validated against a validation set comprising 3 catalysts from the literature and not included in the training set plus one catalyst synthesized by us. Except for one literature catalyst, data in the validation set were predicted with reasonable accuracy. Additionally, a catalyst synthesized by us, for which the MLR model predicted a comonomer incorporation of 4.0%, resulted in a 1-hexene experimental incorporation of 4.5-5%. The trained MLR model was used to predict the comonomer incorporation rate of 10 related zirconocenes having structural features similar to the 19 systems in the training set. We further explored the impact of the precatalyst structure on the comonomer incorporation rate by analyzing a set of 15 zirconocenes having steric and electronic features different from those in the training set. These predictions were validated by DFT calculations.

关键词： multivariate linear regression density functional theory copolymerization ethene 1-olefins group 4 catalyst

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Estimation and Influence Diagnostics for the multivariate linear regression Models with Skew Scale Mixtures of Normal Distributions

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SANKHYA-SERIES B-APPLIED AND INTERDISCIPLINARY STATISTICS 2022年第1期84卷 204-242页

作者： Louredo, Graciliano M. S. Zeller, Camila B. Ferreira, Clecio S. Univ Fed Juiz De Fora Juiz De Fora Brazil

In this paper, we present recent results in the context of multivariate linear regression models considering that random errors follow multivariate skew scale mixtures of normal distributions. This class of distributions includes the scale mixtures of multivariate normal distributions, as special cases, and provides flexibility in capturing a wide variety of asymmetric behaviors. We implemented the algorithm ECM (Expectation/Conditional Maximization) and we obtained closed-form expressions for all the estimators of the parameters of the proposed model. Inspired by the ECM algorithm, we have developed an influence diagnostics for detecting influential observations to investigate the sensitivity of the maximum likelihood estimators. To examine the performance and the usefulness of the proposed methodology, we present simulation studies and analyze a real dataset.

关键词： Skew scale mixtures of normal distributions multivariate linear regression ECM algorithm global and local influence Primary Secondary

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Investigation effects of environmental and operating factors onPVpanel efficiency using by multivariate linear regression

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INTERNATIONAL JOURNAL OF ENERGY RESEARCH 2021年第1期45卷 554-567页

作者： Kaya, Ferhat Sahin, Gokhan Alma, Mehmet Hakki Igdir Univ Mech Engn Dept Igdir Turkey Igdir Univ Elect & Elect Engn Dept TR-76000 Igdir Turkey Kahramanmaras Sutcu Imam Univ Ind Engn Forestry Dept Kahramanmaras Turkey

The aim of this study is to show the investigation effects of environmental and operating factors on photovoltaic (PV) panel efficiency using by multivariate linear regression. Also in this study, the relationship between PV panel efficiency and some environmental and operating factors (solar radiation, open-circuit voltage, short circuit current (I-sc), power, fill factor, outside temperature, humidity, wind speed, and voltage) were investigated using multivariate linear regression. The effect of binary parameter interactions on panel performance was investigated using the backward elimination (or deletion) method. The data used in the analysis were obtained from monocrystal and polycrystal panels in December in the winter season. In all analyzes, the regression values are close to 1, which indicates that the compatibility between binary parameters and performance characteristics is perfect. In addition, the three most effective parameters on panel efficiency were found to be solar radiation, maximum power (P-max), and I-sc, respectively.

关键词： efficiency environmental factors multivariate linear regression photovoltaic module

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Incorporating interaction terms in multivariate linear regression for post-event flood waste estimation

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WASTE MANAGEMENT 2021年 124卷 377-384页

作者： Park, Man Ho Ju, Munsol Jeong, Sangjae Kim, Jae Young Seoul Natl Univ Coll Engn Dept Civil & Environm Engn 1 Gwanak Ro Seoul 08826 South Korea Korea Environm Inst Dept Living Environm Res 370 Sicheong Daero Sejong 30147 South Korea Soonchunhyang Univ Dept Energy & Environm Engn Asan 31538 Chungcheongnam South Korea

multivariate linear regression methodology has been conceived as a viable technique in flood waste estimation. The fundamental assumption of the conventional flood waste model, independence between input variables, may not work in reality. As an alternative, we evaluated the effectiveness of including interaction terms in flood waste modeling. The secondary objectives include to suggest the strategy in flood waste mitigation and to explore a plausible explanation to the modeling results. In the scheme of model development and assessment, ninety flood cases in South Korea were statistically analyzed. Input variables for regression analysis were selected from available datasets in the national disaster information system and the selected variables were flood damage variables used to quantify the amount of flood waste. According to the results, incorporating the interaction terms improved the estimation accuracy of the model. The single-variable sensitivity analysis revealed that mitigating damage to rivers and croplands would most efficiently reduce potential flood waste generation. The interaction terms appeared to compensate for the over/underestimated waste amounts by single terms, and they explained the nonlinear response of waste generation. Observations made throughout the field survey revealed that the nonlinear and interactive pattern of flood waste generation corresponded to the results from the regression analysis. In a practical aspect, incorporating the interaction terms would be an effective method to enhance the flood waste estimation model without costly works for further variables exploration. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： Disaster waste management Field surveying Flood waste estimation Interaction term multivariate linear regression Sensitivity analysis

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Correlation between Vaccination and Child Mortality Rate Using multivariate linear regression Model

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JOURNAL OF INFORMATION & KNOWLEDGE MANAGEMENT 2024年第3期23卷

作者： Revathi, A. Kaladevi, R. Vimaladevi, M. Hariharan, S. Cherukuri, A. K. Sujatha, R. SRM Inst Sci & Technol Kattankulathur Dept Computat Intelligence Chennai Tamil Nadu India Panimalar Engn Coll Dept Informat Technol Chennai Tamil Nadu India Vardhaman Coll Engn Kacharam Hyderabad India Vellore Inst Technol Vellore India SRM Inst Sci & Technol Dept Networking & Commun Kattankulathur Tamil Nadu India

Population has increased drastically over the years and new diseases compete with the population. Immunisation is a preventive measure, which makes the person resistant or immune to the disease. Vaccination stimulates our own immune system against infection or diseases. Vaccines are available for more than twenty life-threatening diseases and it saves millions of lives throughout the world. In the 70th World Assembly conducted in the year 2017, around 194 countries participated and took the oath to strengthen vaccination thereby achieving goals of Global Vaccine Action Plan (GVAP). In spite of remarkable immunisation progress, approximately 20 million infants are not exposed to vaccination every year. The immunisation progress has stalled or even reversed in some countries, and there is a real risk that complacency will undermine past achievements. This paper considered the database of vaccine consumption rate from many countries issued by WHO to analyse the reason for poor access to vaccine with respect to the morality and poverty levels. For this analysis, the relation between vaccine consumption by children below five years, the children's death rate record issued by the United Nations Children's Education Fund (UNICEF), poverty index issued by the United Nations are considered. multivariate linear regression algorithm is used to identify the correlation between datasets. The result shows that an increase in vaccination coverage results in reduction on mortality rate in most of the countries. A correlation coefficient of 0.7 was found between IMR and the vaccine dosages. Sub-Sahara countries' poverty index has direct impact on the declined view of vaccination coverage.

关键词： Immunisation morbidity mortality multivariate linear regression vaccine

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