Robust Linear Model Selection For High Dimensional Datasets PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Robust Linear Model Selection For High Dimensional Datasets PDF full book. Access full book title Robust Linear Model Selection For High Dimensional Datasets.
Author | : Md. Jafar Ahmed Khan |
Publisher | : |
Total Pages | : 155 |
Release | : 2007 |
Genre | : |
ISBN | : 9780494267363 |
Download Robust Linear Model Selection for High-dimensional Datasets Book in PDF, ePub and Kindle
We consider two different strategies for model selection: (a) one-step model building and (b) two-step model building. For one-step model building, we robustify the step-bystep algorithms forward selection (FS) and stepwise (SW), with robust partial F-tests as stopping rules.
Author | : Mengxi Yi |
Publisher | : Springer Nature |
Total Pages | : 500 |
Release | : 2023-04-19 |
Genre | : Mathematics |
ISBN | : 3031226879 |
Download Robust and Multivariate Statistical Methods Book in PDF, ePub and Kindle
This book presents recent developments in multivariate and robust statistical methods. Featuring contributions by leading experts in the field it covers various topics, including multivariate and high-dimensional methods, time series, graphical models, robust estimation, supervised learning and normal extremes. It will appeal to statistics and data science researchers, PhD students and practitioners who are interested in modern multivariate and robust statistics. The book is dedicated to David E. Tyler on the occasion of his pending retirement and also includes a review contribution on the popular Tyler’s shape matrix.
Author | : Le Chang |
Publisher | : |
Total Pages | : 0 |
Release | : 2017 |
Genre | : |
ISBN | : |
Download Essays on Robust Model Selection and Model Averaging for Linear Models Book in PDF, ePub and Kindle
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.
Author | : Ruidi Chen |
Publisher | : |
Total Pages | : 258 |
Release | : 2020-12-23 |
Genre | : Mathematics |
ISBN | : 9781680837728 |
Download Distributionally Robust Learning Book in PDF, ePub and Kindle
Author | : Trevor Hastie |
Publisher | : CRC Press |
Total Pages | : 354 |
Release | : 2015-05-07 |
Genre | : Business & Economics |
ISBN | : 1498712177 |
Download Statistical Learning with Sparsity Book in PDF, ePub and Kindle
Discover New Methods for Dealing with High-Dimensional DataA sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underl
Author | : Steven Brown |
Publisher | : Elsevier |
Total Pages | : 2948 |
Release | : 2020-05-26 |
Genre | : Science |
ISBN | : 0444641661 |
Download Comprehensive Chemometrics Book in PDF, ePub and Kindle
Comprehensive Chemometrics, Second Edition, Four Volume Set features expanded and updated coverage, along with new content that covers advances in the field since the previous edition published in 2009. Subject of note include updates in the fields of multidimensional and megavariate data analysis, omics data analysis, big chemical and biochemical data analysis, data fusion and sparse methods. The book follows a similar structure to the previous edition, using the same section titles to frame articles. Many chapters from the previous edition are updated, but there are also many new chapters on the latest developments. Presents integrated reviews of each chemical and biological method, examining their merits and limitations through practical examples and extensive visuals Bridges a gap in knowledge, covering developments in the field since the first edition published in 2009 Meticulously organized, with articles split into 4 sections and 12 sub-sections on key topics to allow students, researchers and professionals to find relevant information quickly and easily Written by academics and practitioners from various fields and regions to ensure that the knowledge within is easily understood and applicable to a large audience Presents integrated reviews of each chemical and biological method, examining their merits and limitations through practical examples and extensive visuals Bridges a gap in knowledge, covering developments in the field since the first edition published in 2009 Meticulously organized, with articles split into 4 sections and 12 sub-sections on key topics to allow students, researchers and professionals to find relevant information quickly and easily Written by academics and practitioners from various fields and regions to ensure that the knowledge within is easily understood and applicable to a large audience
Author | : Chinghway Lim |
Publisher | : |
Total Pages | : 168 |
Release | : 2011 |
Genre | : |
ISBN | : |
Download Modeling High Dimensional Data Book in PDF, ePub and Kindle
This dissertation is on high dimensional data and their associated regularization through dimension reduction and penalization. We start with two real world problems to illustrate the practical difficulties and remedies in analyzing high dimensional data. In Chapter 1, we are tasked with modeling and predicting the U.S. stock market, where the number of stocks far exceeds the number of days relevant to the current market. Through an existing statistical arbitrage framework, we reduce the dimension of our problem with the use of correspondence analysis. We develop a data driven regression model and highlight some common statistical methods that improve our predictions. In Chapter 2, we attempt to detect and predict system anomalies in large enterprise telephony systems. We do this by processing large amounts of unstructured log files, again with dimension reduction methods, allowing effective visualization and automatic filtering of results. We then move on to more general methodology and analysis in high dimensions. In Chapter 3, we consider regularization methods, often used in dealing with high dimensional data, and tackle the problem of selecting the associated regularization parameter. We introduce SSCV, a selection criterion based on statistical stability, but also incorporating model fit, and show that it can often outperform the popular cross validation. Finally, we explore robust methods in the high dimensional setting in Chapter 4. We focus on the relative performance and distributional robustness of the estimators optimizing L1 and L2 loss functions respectively. We verify some expected results and also highlight cases where results from classical asymptotics fail, setting the stage for future theoretical work.
Author | : Allan D R Mcquarrie |
Publisher | : World Scientific |
Total Pages | : 479 |
Release | : 1998-05-30 |
Genre | : Mathematics |
ISBN | : 9814497045 |
Download Regression And Time Series Model Selection Book in PDF, ePub and Kindle
This important book describes procedures for selecting a model from a large set of competing statistical models. It includes model selection techniques for univariate and multivariate regression models, univariate and multivariate autoregressive models, nonparametric (including wavelets) and semiparametric regression models, and quasi-likelihood and robust regression models. Information-based model selection criteria are discussed, and small sample and asymptotic properties are presented. The book also provides examples and large scale simulation studies comparing the performances of information-based model selection criteria, bootstrapping, and cross-validation selection methods over a wide range of models.
Author | : Julian J. Faraway |
Publisher | : CRC Press |
Total Pages | : 284 |
Release | : 2016-04-19 |
Genre | : Mathematics |
ISBN | : 1439887349 |
Download Linear Models with R Book in PDF, ePub and Kindle
A Hands-On Way to Learning Data AnalysisPart of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models
Author | : Yves Lechevallier |
Publisher | : Springer Science & Business Media |
Total Pages | : 627 |
Release | : 2010-11-08 |
Genre | : Computers |
ISBN | : 3790826049 |
Download Proceedings of COMPSTAT'2010 Book in PDF, ePub and Kindle
Proceedings of the 19th international symposium on computational statistics, held in Paris august 22-27, 2010.Together with 3 keynote talks, there were 14 invited sessions and more than 100 peer-reviewed contributed communications.