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Empirical likelihood ratio test for a change-point in linear regression model

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2008年第16期37卷 2551-2563页

作者： Liu, Yukun Zou, Changliang Zhang, Runchu Nankai Univ LPMC Tianjin 300071 Peoples R China Nankai Univ Sch Math Sci Tianjin 300071 Peoples R China

A nonparametric method based on the empirical likelihood is proposed to detect the change-point in the coefficient of linear regression models. The empirical likelihood ratio test statistic is proved to have the same asymptotic null distribution as that with classical parametric likelihood. Under some mild conditions, the maximum empirical likelihood change-point estimator is also shown to be consistent. The simulation results show the sensitivity and robustness of the proposed approach. The method is applied to some real datasets to illustrate the effectiveness.

关键词： change-point empirical likelihood linear regression model maximum empirical likelihood estimator nonparametric robustness

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Development of statistical linear regression model for metals from transportation land uses

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WATER SCIENCE AND TECHNOLOGY 2009年第12期59卷 2495-2501页

作者： Maniquiz, Marla C. Lee, Soyoung Lee, Eunju Kim, Lee-Hyung Kongju Natl Univ Dept Civil & Environm Engn Cheonan Si Chungnam South Korea

The transportation landuses possessing impervious surfaces such as highways, parking lots, roads, and bridges were recognized as the highly polluted non-point sources (NPSs) in the urban areas. Lots of pollutants from urban transportation are accumulating on the paved surfaces during dry periods and are washed-off during a storm. In Korea, the identification and monitoring of NPSs still represent a great challenge. Since 2004, the Ministry of Environment (MOE) has been engaged in several researches and monitoring to develop stormwater management policies and treatment systems for future implementation. The data over 131 storm events during May 2004 to September 2008 at eleven sites were analyzed to identify correlation relationships between particulates and metals, and to develop simple linear regression (SLR) model to estimate event mean concentration (EMC). Results indicate that there was no significant relationship between metals and TSS EMC. However, the SLR estimation models although not providing useful results are valuable indicators of high uncertainties that NPS pollution possess. Therefore, long term monitoring employing proper methods and precise statistical analysis of the data should be undertaken to eliminate these uncertainties.

关键词： linear regression model metals particulates stormwater runoff transportation

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On the restricted almost unbiased two-parameter estimator in linear regression model

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2017年第4期46卷 1668-1678页

作者： Huang, Hua Wu, Jibo Yi, Wende Chongqing Univ Arts & Sci Sch Math & Finances Chongqing 402160 Peoples R China Chongqing Univ Arts & Sci Key Lab Grp & Graph Theories & Applicat Chongqing Peoples R China

ozkale and Kaciranlar introduced the restricted two-parameter estimator (RTPE) to deal with the well-known multicollinearity problem in linear regression model. In this paper, the restricted almost unbiased two-parameter estimator (RAUTPE) based on the RTPE is presented. The quadratic bias and mean-squared error of the proposed estimator is discussed and compared with the corresponding competitors in literatures. Furthermore, a numerical example and a Monte Carlo simulation study are given to explain some of the theoretical results.

关键词： linear regression model Mean-squared error Restricted two-parameter ridge estimator Primary 62J05 62J07

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Weak consistency of M-estimator in linear regression model with asymptotically almost negatively associated errors

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2020年第11期49卷 2800-2816页

作者： Zhang, Yu Liu, Xinsheng Hu, Hongchang Nanjing Univ Aeronaut & Astronaut State Key Lab Mech Control Mech Struct Inst Nano Sci Nanjing Peoples R China Nanjing Univ Aeronaut & Astronaut Dept Math Nanjing Peoples R China Hubei Normal Univ Sch Math & Stat Huangshi Hubei Peoples R China

This paper studies a linear regression model with asymptotically almost negatively associated (AANA, in short) random errors. Under some mild conditions, the weak consistency of M-estimator of the unknown parameter is investigated, which extend the corresponding results for independent random errors and negatively associated (NA, in short) random errors. At last, two simulation examples are presented to verify the weak consistency of M-estimator in the model.

关键词： Asymptotically almost negatively associated linear regression model M-estimator weak consistency

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Grey Wolf-Based linear regression model for Rainfall Prediction

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INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGIES AND SYSTEMS APPROACH 2022年第1期15卷 1-18页

作者： Mohd, Razeef Butt, Muheet Ahmed Baba, Majid Zaman Univ Kashmir Srinagar Jammu & Kashmir India

This paper develops a rainfall prediction technique, named GWO-based linear regression (GWLR) model, using the linear regression model and grey wolf optimizer (GWO). The linear regression model is used to predict the value of a dependent variable from an independent variable on the basis of regression coefficient. The proposed GWLR predicts rainfall based on the input time-series weather data using the proposed GWLR model, in which the regression coefficients are obtained optimally using the GWO. Thus, the rainfall detection is done on the accumulated data of India and the state Jammu and Kashmir over the years 1901 to 2015. The effectiveness of the proposed GWLR is checked with MSE and PRD values and is evaluated to be the best when compared to other existing techniques with least MSE value as 0.005 and PRD value as 1.700%.

关键词： Grey Wolf Optimizer (GWO) linear regression model Rainfall Prediction regression Coefficients Weather Data

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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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Predicting multivariate response in linear regression model

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2003年第2期32卷 389-409页

作者： Srivastava, MS Solanky, TKS Univ Toronto Dept Stat Toronto ON Canada Univ New Orleans Dept Math New Orleans LA USA

Predicting a multivariate response vector in a linear multivariate regression model requires the estimate of the matrix of regression parameters. Stein (Stein, C. (1973). Estimation of the mean of a multivariate normal distribution. Proc. Prague Symp. Asymp. Statist. 345-381), van der Merwe and Zidek (van der Merwe, A., Zidek;J.V. (1980). Multivariate regression analysis and canonical variates. Canadian Journal of Statistics 8:27-39), Bilodeau and Kariya (Bilodeau, M., Kariya, T. (1989). Minimax estimators in the normal MANOVA model. Journal of Multivariate Analysis 28:260-270) and Konno (Konno, Y. (1990). On estimation of a matrix of mean. Unpublished manuscript;Konno, Y. (1991). On estimation of a matrix of normal means with unknown covariance matrix. J. Multi. Analysis 36:44-55) have shown that their shrinkage estimators perform better than the least squares estimator. Recently, Breiman and Friedman (Breiman, L., Friedman, J. H. (1997). Predicting multivariate responses in multiple regression. J. Roy. Statist. Soc. Ser. B 59:3-54) proposed another class of shrinkage estimators, called C&W-GCV estimators. Through extensive simulations, they have showed that their C&W-GCV estimator performs better than the FICYREG estimator of van der Merwe and Zidek (van der Merwe, A., Zidek, J. V. (1980). Multivariate regression analysis and canonical variates. Canadian Journal of Statistics 8:27-39), the reduced rank regression method of Anderson (Anderson, T. W. (1951). Estimating linear restrictions on regression coefficients for multivariate normal distribution. Ann. Math. Statist., 22:327-351 (Correction in Ann. Statist. (1980), 8, 1400). Estimating linear restrictions on regression coefficients for multivariate normal distribution. Ann. Math. Statist. 22:327-351. (Correction in Ann. Statist. (1980), 8, 1400)), the component-wise ridge regression and the partial least squares. They, however, did not include in their comparisons, the minimax estimators of Bilodeau and Kariya

关键词： multivariate response linear regression model shrinkage estimators simulations

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Reliable metrics-based linear regression model for multilevel privacy measurement of face instances

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IET IMAGE PROCESSING 2022年第7期16卷 1935-1948页

作者： Li, Xuan Huang, Zhenghua Ma, Lei Xu, Yuhang Cheng, Li Yang, Zhi Wuhan Inst Technol Sch Elect & Informat Engn Wuhan Peoples R China Wuhan Inst Technol Hubei Key Lab Opt Informat & Pattern Recognit Wuhan Peoples R China Hubei Univ Technol Sch Comp Sci Wuhan Peoples R China

Social networking sites have made photo sharing convenient and, consequently, users of those sites frequently share photos. The proliferation of these social images throughout the Internet has inadvertently exposed an increasing number of personally identifiable information, particularly from the visual information of the faces in the images. Most existing methods to de-identify faces results in an excessive loss of visual information. To solve this problem, this paper proposes a reliable metrics-based linear regression model for multilevel privacy measurement of face instances using the size information of face instances. The proposed privacy measurement model provides a novel instance-level-based solution to measure privacy levels. The paper also establishes a scientific relationship between the size information of face instances and their privacy levels, quantifying the degree to which face instances need to be de-identified. Finally, the paper proposes a novel k-Same-DT de-identification method to provide reliable metrics for a linear regression model. It is a real-time k-same-related de-identification algorithm that combines the PCA dimensionality reduction strategy and the Delaunay triangle-based face alignment *** proposed k-Same-DT method creates a de-identified face with a lower identifiable rate and higher structural similarity, and it can provide reliable de-identification metrics for privacy measurement. Experiments using the classical face dataset demonstrates the effectiveness of the proposed de-identification method. Extensive experiments and surveys on real-world social images were also conducted to verify the proposed measurement model.

关键词： reliable metrics-based Internet Delaunay triangle-based face alignment algorithm regression analysis face instances social networking (online) multilevel privacy measurement measure privacy levels size information data privacy linear regression model principal component analysis faces results face recognition novel instance-level-based solution visual information classical face dataset social networking sites personally identifiable information privacy measurement model

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Estimating the linear regression model with categorical covariates subject to randomized response

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2006年第11期50卷 3311-3323页

作者： van den Hout, A Kooiman, P Univ Utrecht Fac Social Sci Dept Methodol & Stat NL-3508 TC Utrecht Netherlands CPB Netherlands Bur Econ Policy Anal Dept Labour Market & Welf State NL-2508 GM The Hague Netherlands

The maximum likelihood estimation of the iid normal linear regression model where some of the covariates are subject to randomized response is discussed. Randomized response (RR) is an interview technique that can be used when sensitive questions have to be asked and respondents are reluctant to answer directly. RR variables are described as misclassified categorical variables where conditional misclassification probabilities are known. The likelihood of the linear regression model with RR covariates is derived and a fast and straightforward EM algorithm is developed to obtain maximum likelihood estimates. The basis of the algorithm consists of elementary weighted least-squares steps. A simulation example demonstrates the feasibility of the method. (C) 2005 Elsevier B.V. All rights reserved.

关键词： EM algorithm linear regression model misclassification post randomization method randomized response statistical disclosure control

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Minimax estimation in linear regression model

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 1996年第1期50卷 77-89页

作者： Srivastava, AK Shukla, P UNIV LUCKNOW DEPT STATLUCKNOW 226004UTTAR PRADESHINDIA

Estimation of the coefficient vector of a linear regression model subject to ellipsoidal constraints on the coefficients has been considered. Shrinkage methodology has been synthesized with minimax estimation technique and an estimator based on this has been proposed. The properties of this estimator have been derived under a quadratic loss set-up of the decision theory which are analysed to assess the behaviour of the proposed estimator. Superiority conditions for the dominance of this estimator over the existing minimax and least-squares estimators have also been derived.

关键词： minimax estimation linear regression model inequality and ellipsoidal restrictions regression coefficients mock-minimax and quasi-minimax estimators

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