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Author: Xinyu Zhang
Publisher:
ISBN:
Category :
Languages : en
Pages : 11
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Book Description
This note is in response to a recent paper by Hansen (2007, Econometrica) who proposed an optimal model average estimator with weights selected by minimizing a Mallows criterion. The main contribution of Hansen's paper is a demonstration that the Mallows criterion is asymptotically equivalent to the squared error, so the model average estimator that minimizes the Mallows criterion also minimizes the squared error in large samples. We are concerned with two assumptions that accompany Hansen's approach. First is the assumption that the approximating models are strictly nested in a way that depends on the ordering of regressors. Often there is no clear basis for the ordering and the approach does not permit non-nested models which are more realistic in a practical sense. Second, for the optimality result to hold the model weights are required to lie within a special discrete set. In fact, Hansen (2007) noted both difficulties and called for extensions of the proof techniques. We provide an alternative proof which shows that the result on the optimality of the Mallows criterion in fact holds for continuous model weights and under a non-nested set-up that allows any linear combination of regressors in the approximating models that make up the model average estimator. These are important extensions and our results provide a stronger theoretical basis for the use of the Mallows criterion in model averaging by strengthening existing findings.
Author: Xinyu Zhang
Publisher:
ISBN:
Category :
Languages : en
Pages : 11
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Book Description
This note is in response to a recent paper by Hansen (2007, Econometrica) who proposed an optimal model average estimator with weights selected by minimizing a Mallows criterion. The main contribution of Hansen's paper is a demonstration that the Mallows criterion is asymptotically equivalent to the squared error, so the model average estimator that minimizes the Mallows criterion also minimizes the squared error in large samples. We are concerned with two assumptions that accompany Hansen's approach. First is the assumption that the approximating models are strictly nested in a way that depends on the ordering of regressors. Often there is no clear basis for the ordering and the approach does not permit non-nested models which are more realistic in a practical sense. Second, for the optimality result to hold the model weights are required to lie within a special discrete set. In fact, Hansen (2007) noted both difficulties and called for extensions of the proof techniques. We provide an alternative proof which shows that the result on the optimality of the Mallows criterion in fact holds for continuous model weights and under a non-nested set-up that allows any linear combination of regressors in the approximating models that make up the model average estimator. These are important extensions and our results provide a stronger theoretical basis for the use of the Mallows criterion in model averaging by strengthening existing findings.
Author: Xinyu Zhang
Publisher:
ISBN:
Category :
Languages : en
Pages : 9
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Book Description
This note is in response to a recent paper by Hansen (2007, Econometrica) who proposed an optimal model average estimator with weights selected by minimizing a Mallows criterion. The main contribution of Hansen's paper is a demonstration that the Mallows criterion is asymptotically equivalent to the squared error, so the model average estimator that minimizes the Mallows criterion also minimizes the squared error in large samples. We are concerned with two assumptions that accompany Hansen's approach. First is the assumption that the approximating models are strictly nested in a way that depends on the ordering of regressors. Often there is no clear basis for the ordering and the approach does not permit non-nested models which are more realistic in a practical sense. Second, for the optimality result to hold the model weights are required to lie within a special discrete set. In fact, Hansen (2007) noted both difficulties and called for extensions of the proof techniques. We provide an alternative proof which shows that the result on the optimality of the Mallows criterion in fact holds for continuous model weights and under a non-nested set-up that allows any linear combination of regressors in the approximating models that make up the model average estimator. These are important extensions and our results provide a stronger theoretical basis for the use of the Mallows criterion in model averaging by strengthening existing findings.
Author: Tomohiro Ando
Publisher: CRC Press
ISBN: 9781439836156
Category : Mathematics
Languages : en
Pages : 300
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Book Description
Along with many practical applications, Bayesian Model Selection and Statistical Modeling presents an array of Bayesian inference and model selection procedures. It thoroughly explains the concepts, illustrates the derivations of various Bayesian model selection criteria through examples, and provides R code for implementation. The author shows how to implement a variety of Bayesian inference using R and sampling methods, such as Markov chain Monte Carlo. He covers the different types of simulation-based Bayesian model selection criteria, including the numerical calculation of Bayes factors, the Bayesian predictive information criterion, and the deviance information criterion. He also provides a theoretical basis for the analysis of these criteria. In addition, the author discusses how Bayesian model averaging can simultaneously treat both model and parameter uncertainties. Selecting and constructing the appropriate statistical model significantly affect the quality of results in decision making, forecasting, stochastic structure explorations, and other problems. Helping you choose the right Bayesian model, this book focuses on the framework for Bayesian model selection and includes practical examples of model selection criteria.
Author: Peter Fuleky
Publisher: Springer Nature
ISBN: 3030311503
Category : Business & Economics
Languages : en
Pages : 716
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Book Description
This book surveys big data tools used in macroeconomic forecasting and addresses related econometric issues, including how to capture dynamic relationships among variables; how to select parsimonious models; how to deal with model uncertainty, instability, non-stationarity, and mixed frequency data; and how to evaluate forecasts, among others. Each chapter is self-contained with references, and provides solid background information, while also reviewing the latest advances in the field. Accordingly, the book offers a valuable resource for researchers, professional forecasters, and students of quantitative economics.
Author:
Publisher: ScholarlyEditions
ISBN: 1464965048
Category : Business & Economics
Languages : en
Pages : 1338
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Book Description
Issues in General Economic Research and Application: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about General Economic Research and Application. The editors have built Issues in General Economic Research and Application: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Economic Research and Application in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General Economic Research and Application: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author: Eric D. Feigelson
Publisher: Cambridge University Press
ISBN: 052176727X
Category : Science
Languages : en
Pages : 495
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Book Description
Modern Statistical Methods for Astronomy: With R Applications.
Author: Francesco Ravazzolo
Publisher: Rozenberg Publishers
ISBN: 9051709145
Category :
Languages : en
Pages : 198
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Book Description
Believing in a single model may be dangerous, and addressing model uncertainty by averaging different models in making forecasts may be very beneficial. In this thesis we focus on forecasting financial time series using model averaging schemes as a way to produce optimal forecasts. We derive and discuss in simulation exercises and empirical applications model averaging techniques that can reproduce stylized facts of financial time series, such as low predictability and time-varying patterns. We emphasize that model averaging is not a "magic" methodology which solves a priori problems of poorly forecasting. Averaging techniques have an essential requirement: individual models have to fit data. In the first section we provide a general outline of the thesis and its contributions to previ ous research. In Chapter 2 we focus on the use of time varying model weight combinations. In Chapter 3, we extend the analysis in the previous chapter to a new Bayesian averaging scheme that models structural instability carefully. In Chapter 4 we focus on forecasting the term structure of U.S. interest rates. In Chapter 5 we attempt to shed more light on forecasting performance of stochastic day-ahead price models. We examine six stochastic price models to forecast day-ahead prices of the two most active power exchanges in the world: the Nordic Power Exchange and the Amsterdam Power Exchange. Three of these forecasting models include weather forecasts. To sum up, the research finds an increase of forecasting power of financial time series when parameter uncertainty, model uncertainty and optimal decision making are included.
Author: Fouad Sabry
Publisher: One Billion Knowledgeable
ISBN:
Category : Computers
Languages : en
Pages : 133
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Book Description
What is Least Squares The method of least squares is a parameter estimation method in regression analysis based on minimizing the sum of the squares of the residuals made in the results of each individual equation. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Least squares Chapter 2: Gauss-Markov theorem Chapter 3: Regression analysis Chapter 4: Ridge regression Chapter 5: Total least squares Chapter 6: Ordinary least squares Chapter 7: Weighted least squares Chapter 8: Simple linear regression Chapter 9: Generalized least squares Chapter 10: Linear least squares (II) Answering the public top questions about least squares. (III) Real world examples for the usage of least squares in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Least Squares.
Author: Steve Selvin
Publisher: Oxford University Press
ISBN: 0199747733
Category : Medical
Languages : en
Pages : 477
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Book Description
Statistical analysis typically involves applying theoretically generated techniques to the description and interpretation of collected data. In this text, theory, application and interpretation are combined to present the entire biostatistical process for a series of elementary and intermediate analytic methods. The theoretical basis for each method is discussed with a minimum of mathematics and is applied to a research data example using a computer system called S-PLUS. This system produces concrete numerical results and increases one's understanding of the fundamental concepts and methodology of statistical analysis. Combining statistical logic, data and computer tools, the author explores such topics as random number generation, general linear models, estimation, analysis of tabular data, analysis of variance and survival analysis. The end result is a clear and complete explanation of the way statistical methods can help one gain an understanding of collected data. Modern Applied Biostatistical Methods is unlike other statistical texts, which usually deal either with theory or with applications. It integrates the two elements into a single presentation of theoretical background, data, interpretation, graphics, and implementation. This all-around approach will be particularly helpful to students in various biostatistics and advanced epidemiology courses, and will interest all researchers involved in biomedical data analysis. This text is not a computer manual, even though it makes extensive use of computer language to describe and illustrate applied statistical techniques. This makes the details of the statistical process readily accessible, providing insight into how and why a statistical method identifies the properties of sampled data. The first chapter gives a simple overview of the S-PLUS language. The subsequent chapters use this valuable statistical tool to present a variety of analytic approaches.
Author: David Fletcher
Publisher: Springer
ISBN: 3662585413
Category : Mathematics
Languages : en
Pages : 107
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Book Description
This book provides a concise and accessible overview of model averaging, with a focus on applications. Model averaging is a common means of allowing for model uncertainty when analysing data, and has been used in a wide range of application areas, such as ecology, econometrics, meteorology and pharmacology. The book presents an overview of the methods developed in this area, illustrating many of them with examples from the life sciences involving real-world data. It also includes an extensive list of references and suggestions for further research. Further, it clearly demonstrates the links between the methods developed in statistics, econometrics and machine learning, as well as the connection between the Bayesian and frequentist approaches to model averaging. The book appeals to statisticians and scientists interested in what methods are available, how they differ and what is known about their properties. It is assumed that readers are familiar with the basic concepts of statistical theory and modelling, including probability, likelihood and generalized linear models.
