Download or read book An Adaptive Model Selection Procedure for All subsets Regression written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Adaptive Model Selection Procedure for All subsets Regression microform written by Cheng Kar Wong and published by National Library of Canada = Bibliothèque nationale du Canada. This book was released on 2001 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Adaptive Model Selection written by Yongli Zhang and published by . This book was released on 2007 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Subset Selection in Regression written by Alan Miller and published by CRC Press. This book was released on 2002-04-15 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1990, the first edition of Subset Selection in Regression filled a significant gap in the literature, and its critical and popular success has continued for more than a decade. Thoroughly revised to reflect progress in theory, methods, and computing power, the second edition promises to continue that tradition. The author ha

Download or read book Discrepancy based Algorithms for Best subset Model Selection written by Tao Zhang and published by . This book was released on 2013 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: The selection of a best-subset regression model from a candidate family is a common problem that arises in many analyses. In best-subset model selection, we consider all possible subsets of regressor variables; thus, numerous candidate models may need to be fit and compared. One of the main challenges of best-subset selection arises from the size of the candidate model family: specifically, the probability of selecting an inappropriate model generally increases as the size of the family increases. For this reason, it is usually difficult to select an optimal model when best-subset selection is attempted based on a moderate to large number of regressor variables. Model selection criteria are often constructed to estimate discrepancy measures used to assess the disparity between each fitted candidate model and the generating model. The Akaike information criterion (AIC) and the corrected AIC (AICc) are designed to estimate the expected Kullback-Leibler (K-L) discrepancy. For best-subset selection, both AIC and AICc are negatively biased, and the use of either criterion will lead to overfitted models. To correct for this bias, we introduce a criterion AICi, which has a penalty term evaluated from Monte Carlo simulation. A multistage model selection procedure AICaps, which utilizes AICi, is proposed for best-subset selection. In the framework of linear regression models, the Gauss discrepancy is another frequently applied measure of proximity between a fitted candidate model and the generating model. Mallows' conceptual predictive statistic (Cp) and the modified Cp (MCp) are designed to estimate the expected Gauss discrepancy. For best-subset selection, Cp and MCp exhibit negative estimation bias. To correct for this bias, we propose a criterion CPSi that again employs a penalty term evaluated from Monte Carlo simulation. We further devise a multistage procedure, CPSaps, which selectively utilizes CPSi. In this thesis, we consider best-subset selection in two different modeling frameworks: linear models and generalized linear models. Extensive simulation studies are compiled to compare the selection behavior of our methods and other traditional model selection criteria. We also apply our methods to a model selection problem in a study of bipolar disorder.

Download or read book Adaptive Regression for Modeling Nonlinear Relationships written by George J. Knafl and published by Springer. This book was released on 2016-09-20 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methods for investigating whether relationships are linear or nonlinear and for adaptively fitting appropriate models when they are nonlinear. Data analysts will learn how to incorporate nonlinearity in one or more predictor variables into regression models for different types of outcome variables. Such nonlinear dependence is often not considered in applied research, yet nonlinear relationships are common and so need to be addressed. A standard linear analysis can produce misleading conclusions, while a nonlinear analysis can provide novel insights into data, not otherwise possible. A variety of examples of the benefits of modeling nonlinear relationships are presented throughout the book. Methods are covered using what are called fractional polynomials based on real-valued power transformations of primary predictor variables combined with model selection based on likelihood cross-validation. The book covers how to formulate and conduct such adaptive fractional polynomial modeling in the standard, logistic, and Poisson regression contexts with continuous, discrete, and counts outcomes, respectively, either univariate or multivariate. The book also provides a comparison of adaptive modeling to generalized additive modeling (GAM) and multiple adaptive regression splines (MARS) for univariate outcomes. The authors have created customized SAS macros for use in conducting adaptive regression modeling. These macros and code for conducting the analyses discussed in the book are available through the first author's website and online via the book’s Springer website. Detailed descriptions of how to use these macros and interpret their output appear throughout the book. These methods can be implemented using other programs.

Download or read book Study on Adaptive Model Selection Through Generalized Degrees of Freedom in Nested Linear Regression Models written by 湯泉發 and published by . This book was released on 2010 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Model Selection in All Subsets Regression Via Parametric Bootstrapping written by Chan Keun Park and published by . This book was released on 1999 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Adaptive Subset Selection Via Cost optimization Using Resampling Methods in Linear Regression Models written by Jonnagadda Sunil Rao and published by . This book was released on 1994 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Essays on Robust Model Selection and Model Averaging for Linear Models written by Le Chang and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model selection is central to all applied statistical work. Selecting the variables for use in a regression model is one important example of model selection. This thesis is a collection of essays on robust model selection procedures and model averaging for linear regression models. In the first essay, we propose robust Akaike information criteria (AIC) for MM-estimation and an adjusted robust scale based AIC for M and MM-estimation. Our proposed model selection criteria can maintain their robust properties in the presence of a high proportion of outliers and the outliers in the covariates. We compare our proposed criteria with other robust model selection criteria discussed in previous literature. Our simulation studies demonstrate a significant outperformance of robust AIC based on MM-estimation in the presence of outliers in the covariates. The real data example also shows a better performance of robust AIC based on MM-estimation. The second essay focuses on robust versions of the "Least Absolute Shrinkage and Selection Operator" (lasso). The adaptive lasso is a method for performing simultaneous parameter estimation and variable selection. The adaptive weights used in its penalty term mean that the adaptive lasso achieves the oracle property. In this essay, we propose an extension of the adaptive lasso named the Tukey-lasso. By using Tukey's biweight criterion, instead of squared loss, the Tukey-lasso is resistant to outliers in both the response and covariates. Importantly, we demonstrate that the Tukey-lasso also enjoys the oracle property. A fast accelerated proximal gradient (APG) algorithm is proposed and implemented for computing the Tukey-lasso. Our extensive simulations show that the Tukey-lasso, implemented with the APG algorithm, achieves very reliable results, including for high-dimensional data where p>n. In the presence of outliers, the Tukey-lasso is shown to offer substantial improvements in performance compared to the adaptive lasso and other robust implementations of the lasso. Real data examples further demonstrate the utility of the Tukey-lasso. In many statistical analyses, a single model is used for statistical inference, ignoring the process that leads to the model being selected. To account for this model uncertainty, many model averaging procedures have been proposed. In the last essay, we propose an extension of a bootstrap model averaging approach, called bootstrap lasso averaging (BLA). BLA utilizes the lasso for model selection. This is in contrast to other forms of bootstrap model averaging that use AIC or Bayesian information criteria (BIC). The use of the lasso improves the computation speed and allows BLA to be applied even when the number of variables p is larger than the sample size n. Extensive simulations confirm that BLA has outstanding finite sample performance, in terms of both variable and prediction accuracies, compared with traditional model selection and model averaging methods. Several real data examples further demonstrate an improved out-of-sample predictive performance of BLA.

Download or read book Principles and Theory for Data Mining and Machine Learning written by Bertrand Clarke and published by Springer Science & Business Media. This book was released on 2009-07-21 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extensive treatment of the most up-to-date topics Provides the theory and concepts behind popular and emerging methods Range of topics drawn from Statistics, Computer Science, and Electrical Engineering

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2008 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Robustness of Model Selection Rules written by Jochen A. Jungeilges and published by LIT Verlag Münster. This book was released on 1992 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Adaptive Model Selection in Linear Mixed Models written by Bo Zhang and published by . This book was released on 2009 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Subset Selection in Regression written by Alan J. Miller and published by Springer. This book was released on 2013-08-22 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nearly all statistical packages, and many scientific computing libraries, contain facilities for the empirical choice of a model given a set of data and many variables or alternative models from which to select. There is an abundance of advice on how to perform the mechanics of choosing a model, much of which can only be described as folklore and some of wh ich is quite contradictory. There is a dearth of respectable theory, or even of trustworthy advice, such as recommendations based upon adequate simulations. This mono graph collects together what is known, and presents some new material on estimation. This relates almost entirely to multiple linear regression. The same problems apply to nonlinear regression, such as to the fitting of logistic regressions, to the fitting of autoregressive moving average models, or to any situation in which the same data are to be used both to choose a model and to fit it. This monograph is not a cookbook of recommendations on how to carry out stepwise regression; anyone searching for such advice in its pages will be very disappointed. I hope that it will disturb many readers and awaken them to the dangers in using automatie packages which pick a model and then use least squares to estimate regression coefficients using the same data. My own awareness of these problems was brought horne to me dramatically when fitting models for the prediction of meteorological variables such as temperature or rainfall.

Download or read book ADAPTIVE LASSO FOR MIXED MODEL SELECTION VIA PROFILE LOG LIKELIHOOD written by Juming Pan and published by . This book was released on 2016 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear mixed models describe the relationship between a response variable and some predictors for data that are grouped according to one or more clustering factors. A linear mixed model consists of both fixed effects and random effects. Fixed effects are the conventional linear regression coefficients, and random effects are associated with units which are drawn randomly from a population. By accommodating such two types of parameters, linear mixed models provide an effective and flexible way of representing the means as well as the covariance structure of the data, therefore have been primarily used to model correlated data, and have received much attention in a variety of disciplines including agriculture, biology, medicine, and sociology. Due to the complex nature of the linear mixed models, the selection of only important covariates to create an interpretable model becomes challenging as the dimension of fixed or random effects increases. Thus, determining an appropriate structural form for a model to be used in making inferences and predictions is a fundamental problem in the analysis of longitudinal or clustered data using linear mixed models. This dissertation focuses on selection and estimation for linear mixed models by integrating the recent advances in model selection. More specifically, we propose a two-stage penalized procedure for selecting and estimating important fixed and random effects. Compared with the traditional subset selection approaches, penalized methods can enhance the predictive power of a model, and can significantly reduce computational cost when the number of variables is large (Fan and Li, 2001). Our proposed procedure is different from the existing ones in the literature mainly in two aspects. First, the proposed method is composed of two stages to separately choose the parameters of interests, therefore can respect and accommodate the distinct properties between the random and fixed effects. Second, the usage of the profile log-likelihoods in the selection process can make the computation more efficient and stable due to a smaller number of dimensions involved. In the first stage, we choose the random effects by maximizing the penalized restricted profile log-likelihood, and the maximization is completed by the Newton-Raphson algorithm. Observe that if a random effect is a noise variable, then the corresponding variance components should be all zero. Thus, we first estimate the covariance matrix of random effects using the adaptive LASSO penalized method and then identify the vital ones based on the estimated covariance matrix. In the view of such a selection procedure, the selected random effects are invariant to the selection of the fixed effects. When a proper model for the covariance is adopted, the correct covariance structure will be obtained and valid inferences for the fixed effects can then be achieved in the next stage. We further study the theoretical properties of the proposed procedure for random effects selection. We prove that, with probability tending to one, the proposed procedure surely identifies all true random effects. After the completion of the random effects selection, in the second stage, we select the fixed effects through the maximization of the penalized profile log-likelihood, which only involves the regression coefficients. The optimization of the penalized profile log-likelihood can be solved by the Newton-Raphson algorithm. We then investigate the sampling properties of the resulting estimate of fixed effects. We show that the resulting estimate enjoys model selection oracle properties, indicating that asymptotically the proposed approach can discover the subset of significant predictors. After finishing the two-stage penalized procedure, the best linear mixed model can subsequently be determined and be applied to handle correlated data in a number of fields. To illustrate the performance of the proposed method, numerous simulation studies have been conducted. The simulation results demonstrate that the proposed technique is quite efficient in selecting the best covariates and random covariance structure in linear mixed models and outperforms the existing selection methodologies in general. We finally apply the method to two real data applications for further examining its effectiveness in mixed model selection.

Download or read book Hands On Machine Learning with R written by Brad Boehmke and published by CRC Press. This book was released on 2019-11-07 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hands-on Machine Learning with R provides a practical and applied approach to learning and developing intuition into today’s most popular machine learning methods. This book serves as a practitioner’s guide to the machine learning process and is meant to help the reader learn to apply the machine learning stack within R, which includes using various R packages such as glmnet, h2o, ranger, xgboost, keras, and others to effectively model and gain insight from their data. The book favors a hands-on approach, providing an intuitive understanding of machine learning concepts through concrete examples and just a little bit of theory. Throughout this book, the reader will be exposed to the entire machine learning process including feature engineering, resampling, hyperparameter tuning, model evaluation, and interpretation. The reader will be exposed to powerful algorithms such as regularized regression, random forests, gradient boosting machines, deep learning, generalized low rank models, and more! By favoring a hands-on approach and using real word data, the reader will gain an intuitive understanding of the architectures and engines that drive these algorithms and packages, understand when and how to tune the various hyperparameters, and be able to interpret model results. By the end of this book, the reader should have a firm grasp of R’s machine learning stack and be able to implement a systematic approach for producing high quality modeling results. Features: · Offers a practical and applied introduction to the most popular machine learning methods. · Topics covered include feature engineering, resampling, deep learning and more. · Uses a hands-on approach and real world data.