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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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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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Robust linear regression models:Use of a Stable Distribution for the Response Data

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Open Journal of Statistics 2013年第6期3卷 409-416页

作者： Jorge A.Achcar Angela Achcar Edson Zangiacomi Martinez Medical School University of Sao PauloRibeirao PretoBrazil

In this paper, we study some robustness aspects of linear regression models of the presence of outliers or discordant observations considering the use of stable distributions for the response in place of the usual normality assumption. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, under a Bayesian approach, the use of a latent or auxiliary random variable gives some simplification to obtain any posterior distribution when related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to a standard linear regression model with an explanatory variable and the other is related to a simulated data set assuming a 23 factorial experiment. Posterior summaries of interest are obtained using MCMC (Markov Chain Monte Carlo) methods and the OpenBugs software.

关键词： Stable Distribution Bayesian Analysis linear regression models MCMC Methods OpenBugs Software

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Analyzing the Dissemination of News by Model Averaging and Subsampling

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Journal of Systems Science & Complexity 2024年第5期37卷 2104-2131页

作者： ZOU Jiahui School of Statistics Capital University of Economics and Business

The dissemination of news is a vital topic in management science, social science and data science. With the development of technology, the sample sizes and dimensions of digital news data increase remarkably. To alleviate the computational burden in big data, this paper proposes a method to deal with massive and moderate-dimensional data for linear regression models via combing model averaging and subsampling methodologies. The author first samples a subsample from the full data according to some special probabilities and split covariates into several groups to construct candidate models. Then, the author solves each candidate model and calculates the model-averaging weights to combine these estimators based on this subsample. Additionally, the asymptotic optimality in subsampling form is proved and the way to calculate optimal subsampling probabilities is *** author also illustrates the proposed method via simulations, which shows it takes less running time than that of the full data and generates more accurate estimations than uniform subsampling. Finally,the author applies the proposed method to analyze and predict the sharing number of news, and finds the topic, vocabulary and dissemination time are the determinants.

关键词： Asymptotic optimality dissemination of news linear regression models model averaging optimal subsampling

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Estimates for Lyme borreliosis infections based on models using sentinel canine and human seroprevalence data

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Infectious Disease Modelling 2020年第1期5卷 871-888页

作者： Michael J.Cook Basant K.Puri Vis a Vis Symposiums Bury St EdmundsUK CAR CambridgeUK

Two models were developed to estimate Lyme borreliosis(LB)*** was based on the seroprevalence of Borrelia infections in human *** model used corrections for false negative and false positive results from published test sensitivity and specificity measures.A second model based on Borrelia infections in sentinel dogs was used to quantify the prevalence of Lyme disease Borrelia infections in humans;the reference baseline for this model was human and canine infections in Germany.A comparison of the two models is shown and differences *** relationships between incidence,prevalence and total infection burden for LB were derived from published data and these were used in both models to calculate annual incidence,prevalence and total LB *** modelling was conservative and based on medical insurance records coded for erythema *** model growth rates were used in place of the commonly adopted exponential *** mean of the two models was used to create estimates for various countries and *** from the analyses for LB estimated for 2018 include:incidence e USA 473,000/year,Germany 471,000/year,France 434,000/year and UK 132,000/year;prevalence e USA 2.4 million,Germany 2.4 million,France 2.2 million and UK 667,000;total infections e USA 10.1 million,Germany 10.0 million,France 9.3 million and UK 2.8 *** for the world for 2018 are:incidence 12.3 million/year;prevalence 62.1 million;and total infection burden 262.0 *** figures are far higher than officially published data and reflect not only the underestimation of diagnosed cases,which is acknowledged by health agencies,but also undiagnosed and misdiagnosed cases.

关键词： Lyme disease Borreliosis linear regression models Seropositive Companion animals Sentinel animals

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