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Dynamic Variable Selection In High Dimensional Predictive Regressions
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Book Synopsis Dynamic Variable Selection in High-Dimensional Predictive Regressions by : Daniele Bianchi
Download or read book Dynamic Variable Selection in High-Dimensional Predictive Regressions written by Daniele Bianchi and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop methodology and theory for a general Bayesian approach towards dynamic variable selection in high-dimensional regression models with time-varying parameters. Specifically, we propose a variational inference scheme which features dynamic sparsity-inducing properties so that different subsets of "active'' predictors can be identified over different time periods. We compare our modeling framework against established static and dynamic variable selection methods both in simulation and within the context of two common problems in macroeconomics and finance: inflation forecasting and equity returns predictability. The results show that our approach helps to tease out more accurately the dynamic impact of different predictors over time. This translates into significant gains in terms of out-of-sample point and density forecasting accuracy. We believe our results highlight the importance of taking a dynamic approach towards variable selection for economic modeling and forecasting.
Book Synopsis Boosting Methods for Variable Selection in High Dimensional Sparse Models by :
Download or read book Boosting Methods for Variable Selection in High Dimensional Sparse Models written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Firstly, we propose new variable selection techniques for regression in high dimensional linear models based on a forward selection version of the LASSO, adaptive LASSO or elastic net, respectively to be called as forward iterative regression and shrinkage technique (FIRST), adaptive FIRST and elastic FIRST. These methods seem to work better for an extremely sparse high dimensional linear regression model. We exploit the fact that the LASSO, adaptive LASSO and elastic net have closed form solutions when the predictor is one-dimensional. The explicit formula is then repeatedly used in an iterative fashion until convergence occurs. By carefully considering the relationship between estimators at successive stages, we develop fast algorithms to compute our estimators. The performance of our new estimators is compared with commonly used estimators in terms of predictive accuracy and errors in variable selection. It is observed that our approach has better prediction performance for highly sparse high dimensional linear regression models. Secondly, we propose a new variable selection technique for binary classification in high dimensional models based on a forward selection version of the Squared Support Vector Machines or one-norm Support Vector Machines, to be called as forward iterative selection and classification algorithm (FISCAL). This methods seem to work better for a highly sparse high dimensional binary classification model. We suggest the squared support vector machines using 1-norm and 2-norm simultaneously. The squared support vector machines are convex and differentiable except at zero when the predictor is one-dimensional. Then an iterative forward selection approach is applied along with the squared support vector machines until a stopping rule is satisfied. Also, we develop a recursive algorithm for the FISCAL to save computational burdens. We apply the processes to the original onenorm Support Vector Machines. We compare the FISCAL with other widely used.
Book Synopsis Variable Selection in High Dimensional Linear Regressions with Parameter Instability by : Alexander Chudik
Download or read book Variable Selection in High Dimensional Linear Regressions with Parameter Instability written by Alexander Chudik and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with the problem of variable selection when the marginal effects of signals on the target variable as well as the correlation of the covariates in the active set are allowed to vary over time, without committing to any particular model of parameter instabilities. It poses the issue of whether weighted or unweighted observations should be used at the variable selection stage in the presence of parameter instability, particularly when the number of potential covariates is large. Amongst the extant variable selection approaches, we focus on the One Covariate at a time Multiple Testing (OCMT) method. This procedure allows a natural distinction between the selection and forecasting stages. We establish three main theorems on selection, estimation post selection, and in-sample fit. These theorems provide justification for using unweighted observations at the selection stage of OCMT and down-weighting of observations only at the forecasting stage. The benefits of the proposed method as compared to Lasso, Adaptive Lasso and Boosting are illustrated by Monte Carlo studies and empirical applications to forecasting monthly stock market returns and quarterly output growths.
Book Synopsis Variable Selection and Forecasting in High Dimensional Linear Regressions with Structural Breaks by : Alexander Chudik
Download or read book Variable Selection and Forecasting in High Dimensional Linear Regressions with Structural Breaks written by Alexander Chudik and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with problem of variable selection and forecasting in the presence of parameter instability. There are a number of approaches proposed for forecasting in the presence of breaks, including the use of rolling windows or exponential down-weighting. However, these studies start with a given model specification and do not consider the problem of variable selection. It is clear that, in the absence of breaks, researchers should weigh the observations equally at both variable selection and forecasting stages. In this study, we investigate whether or not we should use weighted observations at the variable selection stage in the presence of structural breaks, particularly when the number of potential covariates is large. Amongst the extant variable selection approaches we focus on the recently developed One Covariate at a time Multiple Testing (OCMT) method that allows a natural distinction between the selection and forecasting stages, and provide theoretical justification for using the full (not down-weighted) sample in the selection stage of OCMT and down-weighting of observations only at the forecasting stage (if needed). The benefits of the proposed method are illustrated by empirical applications to forecasting output growths and stock market returns.
Book Synopsis Variable Selection in High Dimensional Complex Data and Bayesian Estimation of Reduction Subspace by : Moumita Karmakar
Download or read book Variable Selection in High Dimensional Complex Data and Bayesian Estimation of Reduction Subspace written by Moumita Karmakar and published by . This book was released on 2015 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays researchers are collecting large amount of data for which the number of predictors p is often too large to allow a thorough graphical visualization of the data for regression modeling. Commonly regression data are collected jointly on (Y, X) where X = (X1, ⋯, Xp)T is a random p-dimensional predictor and Y is a univariate response. In high dimensional setup, frequently encountered problems for variable selection or estimation in regression analyses are i) nonlinear relationship among predictors and response, ii) number of predictors much larger than sample size, iii) presence of sparsity.
Book Synopsis Dynamic Factor Models by : Siem Jan Koopman
Download or read book Dynamic Factor Models written by Siem Jan Koopman and published by Emerald Group Publishing. This book was released on 2016-01-08 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores dynamic factor model specification, asymptotic and finite-sample behavior of parameter estimators, identification, frequentist and Bayesian estimation of the corresponding state space models, and applications.
Book Synopsis Forecasting with Exponential Smoothing by : Rob Hyndman
Download or read book Forecasting with Exponential Smoothing written by Rob Hyndman and published by Springer Science & Business Media. This book was released on 2008-06-19 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exponential smoothing methods have been around since the 1950s, and are still the most popular forecasting methods used in business and industry. However, a modeling framework incorporating stochastic models, likelihood calculation, prediction intervals and procedures for model selection, was not developed until recently. This book brings together all of the important new results on the state space framework for exponential smoothing. It will be of interest to people wanting to apply the methods in their own area of interest as well as for researchers wanting to take the ideas in new directions. Part 1 provides an introduction to exponential smoothing and the underlying models. The essential details are given in Part 2, which also provide links to the most important papers in the literature. More advanced topics are covered in Part 3, including the mathematical properties of the models and extensions of the models for specific problems. Applications to particular domains are discussed in Part 4.
Book Synopsis Variable Selection and Dimension Reduction in High-dimensional Regression by : Tao Wang
Download or read book Variable Selection and Dimension Reduction in High-dimensional Regression written by Tao Wang and published by . This book was released on 2013 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dynamic Factor Models by : Jörg Breitung
Download or read book Dynamic Factor Models written by Jörg Breitung and published by . This book was released on 2005 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Regularization Approach for Estimation and Variable Selection in High Dimensional Regression by : Yiannis Dendramis
Download or read book A Regularization Approach for Estimation and Variable Selection in High Dimensional Regression written by Yiannis Dendramis and published by . This book was released on 2019 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model selection and estimation are important topics in econometric analysis which can become considerably complicated in high dimensional settings, where the set of possible regressors can become larger than the set of available observations. For large scale problems the penalized regression methods (e.g. Lasso) have become the de facto benchmark that can effectively trade off parsimony and fit. In this paper we introduce a regularized estimation and model selection approach that is based on sparse large covariance matrix estimation, introduced by Bickel and Levina (2008) and extended by Dendramis, Giraitis, and Kapetanios (2018). We provide asymptotic and small sample results that indicate that our approach can be an important alternative to the penalized regression. Moreover, we also introduce a number of extensions that can improve the asymptotic and small sample performance of the proposed method. The usefulness of what we propose is illustrated via Monte Carlo exercises and an empirical application in macroeconomic forecasting.
Book Synopsis High-dimensional Variable Selection for Spatial Regression and Covariance Estimation by : Siddhartha Nandy
Download or read book High-dimensional Variable Selection for Spatial Regression and Covariance Estimation written by Siddhartha Nandy and published by . This book was released on 2016 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Economic Forecasting by : Graham Elliott
Download or read book Handbook of Economic Forecasting written by Graham Elliott and published by Elsevier. This book was released on 2013-08-23 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: The highly prized ability to make financial plans with some certainty about the future comes from the core fields of economics. In recent years the availability of more data, analytical tools of greater precision, and ex post studies of business decisions have increased demand for information about economic forecasting. Volumes 2A and 2B, which follows Nobel laureate Clive Granger's Volume 1 (2006), concentrate on two major subjects. Volume 2A covers innovations in methodologies, specifically macroforecasting and forecasting financial variables. Volume 2B investigates commercial applications, with sections on forecasters' objectives and methodologies. Experts provide surveys of a large range of literature scattered across applied and theoretical statistics journals as well as econometrics and empirical economics journals. The Handbook of Economic Forecasting Volumes 2A and 2B provide a unique compilation of chapters giving a coherent overview of forecasting theory and applications in one place and with up-to-date accounts of all major conceptual issues. Focuses on innovation in economic forecasting via industry applications Presents coherent summaries of subjects in economic forecasting that stretch from methodologies to applications Makes details about economic forecasting accessible to scholars in fields outside economics
Book Synopsis Variable Selection in High Dimensional Data Analysis with Applications by :
Download or read book Variable Selection in High Dimensional Data Analysis with Applications written by and published by . This book was released on 2015 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Variable Selection Via Penalized Regression and the Genetic Algorithm Using Information Complexity, with Applications for High-dimensional -omics Data by : Tyler J. Massaro
Download or read book Variable Selection Via Penalized Regression and the Genetic Algorithm Using Information Complexity, with Applications for High-dimensional -omics Data written by Tyler J. Massaro and published by . This book was released on 2016 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is a collection of examples, algorithms, and techniques for researchers interested in selecting influential variables from statistical regression models. Chapters 1, 2, and 3 provide background information that will be used throughout the remaining chapters, on topics including but not limited to information complexity, model selection, covariance estimation, stepwise variable selection, penalized regression, and especially the genetic algorithm (GA) approach to variable subsetting. In chapter 4, we fully develop the framework for performing GA subset selection in logistic regression models. We present advantages of this approach against stepwise and elastic net regularized regression in selecting variables from a classical set of ICU data. We further compare these results to an entirely new procedure for variable selection developed explicitly for this dissertation, called the post hoc adjustment of measured effects (PHAME). In chapter 5, we reproduce many of the same results from chapter 4 for the first time in a multinomial logistic regression setting. The utility and convenience of the PHAME procedure is demonstrated on a set of cancer genomic data. Chapter 6 marks a departure from supervised learning problems as we shift our focus to unsupervised problems involving mixture distributions of count data from epidemiologic fields. We start off by reintroducing Minimum Hellinger Distance estimation alongside model selection techniques as a worthy alternative to the EM algorithm for generating mixtures of Poisson distributions. We also create for the first time a GA that derives mixtures of negative binomial distributions. The work from chapter 6 is incorporated into chapters 7 and 8, where we conclude the dissertation with a novel analysis of mixtures of count data regression models. We provide algorithms based on single and multi-target genetic algorithms which solve the mixture of penalized count data regression models problem, and we demonstrate the usefulness of this technique on HIV count data that were used in a previous study published by Gray, Massaro et al. (2015) as well as on time-to-event data taken from the cancer genomic data sets from earlier.
Book Synopsis The Oxford Handbook of Economic Forecasting by : Michael P. Clements
Download or read book The Oxford Handbook of Economic Forecasting written by Michael P. Clements and published by OUP USA. This book was released on 2011-07-08 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: Greater data availability has been coupled with developments in statistical theory and economic theory to allow more elaborate and complicated models to be entertained. These include factor models, DSGE models, restricted vector autoregressions, and non-linear models.
Book Synopsis Variable Selection for High-dimensional Data with Error Control by : Han Fu (Ph. D. in biostatistics)
Download or read book Variable Selection for High-dimensional Data with Error Control written by Han Fu (Ph. D. in biostatistics) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many high-throughput genomic applications involve a large set of covariates and it is crucial to discover which variables are truly associated with the response. It is often desirable for researchers to select variables that are indeed true and reproducible in followup studies. Effectively controlling the false discovery rate (FDR) increases the reproducibility of the discoveries and has been a major challenge in variable selection research, especially for high-dimensional data. Existing error control approaches include augmentation approaches which utilize artificial variables as benchmarks for decision making, such as model-X knockoffs. We introduce another augmentation-based selection framework extended from a Bayesian screening approach called reference distribution variable selection. Ordinal responses, which were not previously considered in this area, were used to compare different variable selection approaches. We constructed various importance measures that fit into the selection frameworks, using either L1 penalized regression or machine learning techniques, and compared these measures in terms of the FDR and power using simulated data. Moreover, we applied these selection methods to high-throughput methylation data for identifying features associated with the progression from normal liver tissue to hepatocellular carcinoma to further compare and contrast their performances. Having established the effectiveness of FDR control for model-X knockoffs, we turned our attention to another important data type - survival data with long-term survivors. Medical breakthroughs in recent years have led to cures for many diseases, resulting in increased observations of long-term survivors. The mixture cure model (MCM) is a type of survival model that is often used when a cured fraction exists. Unfortunately, currently few variable selection methods exist for MCMs when there are more predictors than samples. To fill the gap, we developed penalized MCMs for high-dimensional datasets which allow for identification of prognostic factors associated with both cure status and/or survival. Both parametric models and semi-parametric proportional hazards models were considered for modeling the survival component. For penalized parametric MCMs, we demonstrated how the estimation proceeded using two different iterative algorithms, the generalized monotone incremental forward stagewise (GMIFS) and Expectation-Maximization (E-M). For semi-parametric MCMs where multiple types of penalty functions were considered, the coordinate descent algorithm was combined with E-M for optimization. The model-X knockoffs method was combined with these algorithms to allow for FDR control in variable selection. Through extensive simulation studies, our penalized MCMs have been shown to outperform alternative methods on multiple metrics and achieve high statistical power with FDR being controlled. In two acute myeloid leukemia (AML) applications with gene expression data, our proposed approaches identified important genes associated with potential cure or time-to-relapse, which may help inform treatment decisions for AML patients.
Book Synopsis Topics on Variable Selection in High-Dimensional Data by : Jia Wang
Download or read book Topics on Variable Selection in High-Dimensional Data written by Jia Wang and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Variable selection has been extensively studied in the last few decades as it provides a principled solution to high dimensionality arising in a broad spectrum of real applications, such as bioinformatics, health studies, social science and econometrics. This dissertation is concerned with variable selection for ultrahigh-dimensional data when the dimension is allowed to grow with the sample size or the network size at an exponential rate. We propose new Bayesian approaches to selecting variables under several model frameworks, including (1) partially linear models (2) static social network models with degree heterogeneity and (3) time-varying network models. Firstly for partially linear models, we develop a procedure which employs the difference-based method to reduce the impact from the estimation of the nonparametric component, and incorporates Bayesian subset modeling with diffusing prior (BSM-DP) to shrink the corresponding estimator in the linear component. Secondly, a class of network models where the connection probability depends on ultrahigh-dimensional nodal covariates (homophily) and node-specific popularity (degree heterogeneity) is considered. We propose a Bayesian method to select nodal features in both dense and sparse networks under a relaxed assumption on popularity parameters. To alleviate the computational burden for large sparse networks, we particularly develop another working model in which parameters are updated based on a dense sub-graph at each step. Lastly, we extend the static model to time-varying cases, where the connection probability at time t is modeled based on observed nodal attributes at time t and node-specific continuous-time baseline functions evaluated at time t. Those Bayesian proposals are shown to be analogous to a mixture of L0 and L2 penalized methods and work well in the setting of highly correlated predictors. Corresponding model selection consistency is studied for all aforementioned models, in the sense that the probability of the true model being selected converges to one asymptotically. The finite sample performance of the proposed models is further examined by simulation studies and analyses on social-media and financial datasets.
