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Penalized Lq-likelihood estimators and variable selection in linear regression models

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2022年第17期51卷 5957-5970页

作者： Hu, Hongchang Zeng, Zhen Hubei Normal Univ Sch Math & Stat Huangshi 435002 Hubei Peoples R China Nanjin Univ Finana & Econ Sch Appl Math Nanjing Peoples R China

Consider a linear regression model yi = x(i)(T) beta + e(i), i = 1,2,..., n, where {e(i)} are independent identically distributed (iid) random variables with zero mean and known variance sigma(2). Based on the maximum Lq-likelihood estimator (MLqE) and the penalized likelihood estimator (PLE), we introduce a new parametric estimator which is called penalized Lq-likelihood estimator (PLqE). We investigate its Oracle properties and influence function. Simulation results support the validity of our approach. Furthermore, it is shown that the PLqE is robust, while the PLE is not.

关键词： linear regression models penalized Lq-likelihood estimators oracle properties influence function

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With Great Dispersion Comes Greater Resilience: Efficient Poisoning Attacks and Defenses for linear regression models

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IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 2021年 16卷 3709-3723页

作者： Wen, Jialin Zhao, Benjamin Zi Hao Xue, Minhui Oprea, Alina Qian, Haifeng East China Normal Univ Sch Comp Sci Technol Shanghai 200062 Peoples R China East China Normal Univ Software Engn Inst Shanghai 200062 Peoples R China Univ New South Wales CSIRO Data61 Sydney NSW 2052 Australia Univ Adelaide Sch Comp Sci Adelaide SA 5005 Australia Northeastern Univ Khoury Coll Comp Sci Boston MA 02115 USA

With the rise of third parties in the machine learning pipeline, the service provider in "Machine Learning as a Service" (MLaaS), or external data contributors in online learning, or the retraining of existing models, the need to ensure the security of the resulting machine learning models has become an increasingly important topic. The security community has demonstrated that without transparency of the data and the resulting model, there exist many potential security risks, with new risks constantly being discovered. In this paper, we focus on one of these security risks - poisoning attacks. Specifically, we analyze how attackers may interfere with the results of regression learning by poisoning the training datasets. To this end, we analyze and develop a new poisoning attack algorithm. Our attack, termed Nopt, in contrast with previous poisoning attack algorithms, can produce larger errors with the same proportion of poisoning data-points. Furthermore, we also significantly improve the state-of-the-art defense algorithm, termed TRIM, proposed by Jagielsk et al. (IEEE S&P 2018), by incorporating the concept of probability estimation of clean data-points into the algorithm. Our new defense algorithm, termed Proda, demonstrates an increased effectiveness in reducing errors arising from the poisoning dataset through optimizing ensemble models. We highlight that the time complexity of TRIM had not been estimated;however, we deduce from their work that TRIM can take exponential time complexity in the worst-case scenario, in excess of Proda's logarithmic time. The performance of both our proposed attack and defense algorithms is extensively evaluated on four real-world datasets of housing prices, loans, health care, and bike sharing services. We hope that our work will inspire future research to develop more robust learning algorithms immune to poisoning attacks.

关键词： Training linear regression Data models Predictive models Numerical models Machine learning Time complexity Data poisoning attacks and defenses linear regression models complexity

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Sign-Perturbed Sums: A New System Identification Approach for Constructing Exact Non-Asymptotic Confidence Regions in linear regression models

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2015年第1期63卷 169-181页

作者： Csaji, Balazs Csanad Campi, Marco Claudio Weyer, Erik Hungarian Acad Sci MTA SZTAKI Inst Comp Sci & Control H-1111 Budapest Hungary Univ Brescia Dept Informat Engn I-25123 Brescia Italy Univ Melbourne Dept Elect & Elect Engn Melbourne Vic 3010 Australia

We propose a new system identification method, called Sign-Perturbed Sums (SPS), for constructing non-asymptotic confidence regions under mild statistical assumptions. SPS is introduced for linear regression models, including but not limited to FIR systems, and we show that the SPS confidence regions have exact confidence probabilities, i.e., they contain the true parameter with a user-chosen exact probability for any finite data set. Moreover, we also prove that the SPS regions are star convex with the Least-Squares (LS) estimate as a star center. The main assumptions of SPS are that the noise terms are independent and symmetrically distributed about zero, but they can be nonstationary, and their distributions need not be known. The paper also proposes a computationally efficient ellipsoidal outer approximation algorithm for SPS. Finally, SPS is demonstrated through a number of simulation experiments.

关键词： Finite sample properties least squares methods linear regression models parameter estimation statistics system identification

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Bayesian sensitivity analysis in elliptical linear regression models

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2000年第1期86卷 175-199页

作者： Arellano-Valle, RB Galea-Rojas, M Zuazola, PI Pontificia Univ Catolica Chile Fac Matemat Dept Estadist Santiago Chile Univ Valparaiso Valparaiso Chile

Bayesian influence measures for linear regression models have been developed mostly for normal regression models with noninformative prior distributions for the unknown parameters. In this work we extend existing results in several directions. First, we review influence measures for the ordinary normal regression model under conjugate prior distributions in unified framework. Second, we consider elliptical regression models with noninformative prior distributions for the model parameters and investigate the influence of a given subset of observations on the posterior distributions of the location and scale parameters. We found that these influence measures are Bayesian versions of classical counterparts to identify outliers or influential observations. Finally, we show that departures from normality within the multivariate elliptical family of distributions only affect the posterior distribution of the scale parameter. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： linear regression models elliptical distributions influence measures Bayes risks L-1-distance J-distance

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Statistical inference for linear regression models with additive distortion measurement errors

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STATISTICAL PAPERS 2020年第6期61卷 2483-2509页

作者： Feng, Zhenghui Zhang, Jun Chen, Qian Xiamen Univ Sch Econ Xiamen 361005 Peoples R China Xiamen Univ Wang Yanan Inst Studies Econ Xiamen 361005 Peoples R China Shenzhen Univ Coll Math & Stat Shenzhen Hong Kong Joint Res Ctr Appl Stat Sci Inst Stat Sci Shenzhen Peoples R China Shenzhen Univ Coll Math & Stat Shenzhen Peoples R China

We consider estimations and hypothesis test for linear regression measurement error models when the response variable and covariates are measured with additive distortion measurement errors, which are unknown functions of a commonly observable confounding variable. In the parameter estimation and testing part, we first propose a residual-based least squares estimator under unrestricted and restricted conditions. Then, to test a hypothesis on the parametric components, we propose a test statistic based on the normalized difference between residual sums of squares under the null and alternative hypotheses. We establish asymptotic properties for the estimators and test statistics. Further, we employ the smoothly clipped absolute deviation penalty to select relevant variables. The resulting penalized estimators are shown to be asymptotically normal and have the oracle property. In the model checking part, we suggest two test statistics for checking the validity of linear regression models. One is a score-type test statistic and the other is a model- adaptive test statistic. The quadratic form of the scaled test statistic is asymptotically chi-squared distributed under the null hypothesis and follows a noncentral chi-squared distribution under local alternatives that converge to the null hypothesis. We also conduct simulation studies to demonstrate the performance of the proposed procedure and analyze a real example for illustration.

关键词： Measurement errors Kernel smoothing linear regression models Residual based estimator Model Checking

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Robust tests for change in intercept and slope in linear regression models with application to manager performance in the mutual fund industry

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ECONOMIC MODELLING 2016年 58卷 523-534页

作者： Pouliot, William Univ Birmingham Dept Econ Birmingham B15 2TT W Midlands England

Financial as well as economic theory have developed models which can be used to evaluate performance of mutual funds and that can assist regulators in monitoring performance of financial markets. These models make use of linear regressions models to provide this information. In particular, interest lies with the intercept parameter of these models and whether it is time varying. In applications to mutual fund performance, time varying alpha indicates a change in manager's stock selecting abilities. In applications to regulation of financial markets, time-varying alpha indicates potential changes to equity returns based on undisclosed information. These are importance concerns and emphasize the need to have accurate methods to disentangle changes in intercept from slope in these models. Here, a novel bivariate statistic is developed that can be used for this purpose. It has many attractive features. For example, the use of weight functions improves its power for discrete changes in intercept/slope that occur late/early in the sample, allows intercept/slope to change at different dates, allows for control of global error rates;and avoids trimming. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Structural break tests CUSUM tests linear regression models U-statistics Mutual fund performance

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Two New Relative Efficiencies of the Weighted Mixed Estimator with Respect to the Ordinary Least Squares Estimator in linear regression models

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Journal of Mathematical Research with Applications 2016年第1期36卷 109-116页

作者： Min LI Jibo WU School of Mathematics and Finances Chongqing University of Arts and Sciences Key Laboratory of Group & Graph Theories and Applications Chongqing University of Arts and Sciences

In this paper, we present two relative efficiency of the weighted mixed estimator in respect of least squares estimator. We also derive the lower and upper bounds of those relative efficiencies.

关键词： ordinary least squares estimator weighted mixed estimator relative efficiency linear regression models

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Iterative weighted estimation based on variance modelling in linear regression models

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2019年第9期48卷 2599-2614页

作者： Zhao, Yan-Yong Lin, Jin-Guan Huang, Xing-Fang Wang, Hong-Xia Nanjing Audit Univ Sch Stat & Math Nanjing 211815 Jiangsu Peoples R China

The estimation of variance function plays an extremely important role in statistical inference of the regression models. In this paper we propose a variance modelling method for constructing the variance structure via combining the exponential polynomial modelling method and the kernel smoothing technique. A simple estimation method for the parameters in heteroscedastic linear regression models is developed when the covariance matrix is unknown diagonal and the variance function is a positive function of the mean. The consistency and asymptotic normality of the resulting estimators are established under some mild assumptions. In particular, a simple version of bootstrap test is adapted to test misspecification of the variance function. Some Monte Carlo simulation studies are carried out to examine the finite sample performance of the proposed methods. Finally, the methodologies are illustrated by the ozone concentration dataset.

关键词： Asymptotic properties linear regression models Modified Levenberg-Marquardt method Variance modelling

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Productivity linear regression models of Tree-Length Harvesting System in Natural Coastal Aleppo Pine (Pinus halepensis L.) Forests in the Chalkidiki Area of Greece

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CROATIAN JOURNAL OF FOREST ENGINEERING 2012年第1期33卷 115-123页

作者： Gallis, Christos Spyroglou, Gavriil Forest Res Inst Thessaloniki 57006 Greece

Time studies of harvesting and skidding tree-length logs in Aleppo pine (Pinus halepensis L.) natural coastal forests of Chalkidiki area in northern Greece were carried out to formulate linear regression models and to evaluate productivity. The harvesting system consisted of a feller with chainsaw for felling, delimbing and crosscutting, and a four wheel drive farm tractor, with a 74 kW engine, equipped with a special winch attached to the tractor three point hitch for the extraction of tree length logs. Operational factors such as distance, slope, volume and the time required for harvesting and extracting tree length logs were measured and recorded. The results illustrate that the calibrated linear regression models show strong correlation between the time needed for harvesting operations and the extraction distance from the stump to the forest road.

关键词： tree length system extraction time studies linear regression models productivity Aleppo pine natural coastal forests

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Dverview and Main Advances in Permutation Tests for linear regression models

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Journal of Mathematics and System Science 2015年第2期5卷 53-59页

作者： Massimiliano Giacalone Angela Alibrandi School of Economics Management and Statistics Bologna University Piazza Scaravilli 2 Bologna Italy. Department of Economical Business and Environmental Sciences and Quantitative Methods Messina University Via dei Verdi 75Messina ltaly.

When the population, from which the samples are extracted, is not normally distributed, or if the sample size is particularly reduced, become preferable the use of not parametric statistic test. An alternative to the normal model is the permutation or randomization model. The permutation model is nonparametric because no formal assumptions are made about the population parameters of the reference distribution, i.e., the distribution to which an obtained result is compared to determine its probability when the null hypothesis is true. Typically the reference distribution is a sampling distribution for parametric tests and a permutation distribution for many nonparametric tests. Within the regression models, it is possible to use the permutation tests, considering their ownerships of optimality, especially in the multivariate context and the normal distribution of the response variables is not guaranteed. In the literature there are numerous permutation tests applicable to the estimation of the regression models. The purpose of this study is to examine different kinds of permutation tests applied to linear models, focused our attention on the specific test statistic on which they are based. In this paper we focused our attention on permutation test of the independent variables, proposed by Oja, and other methods to effect the inference in non parametric way, in a regression model. Moreover, we show the recent advances in this context and try to compare them.

关键词： Permutation Tests linear regression models Non Parametric Approach.

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