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Andresen and Spokoiny's (2013) "critical dimension in semiparametric estimation" provide a technique for the finite sample analysis of profile M-estimators. This paper uses very similar ideas to derive two convergence results for the alternating procedure to approximate the maximizer of random functionals such as the realized log likelihood in MLE estimation. We manage to show that the sequence attains the same deviation properties as shown for the profile M-estimator in Andresen and Spokoiny (2013), i.e. a finite sample Wilks and Fisher theorem. Further under slightly stronger smoothness constraints on the random functional we can show nearly linear convergence to the global maximizer if the starting point for the procedure is well chosen.
The aim of this textbook (previously titled SAS for Data Analytics) is to teach the use of SAS for statistical analysis of data for advanced undergraduate and graduate students in statistics, data science, and disciplines involving analyzing data. The book begins with an introduction beyond the basics of SAS, illustrated with non-trivial, real-world, worked examples. It proceeds to SAS programming and applications, SAS graphics, statistical analysis of regression models, analysis of variance models, analysis of variance with random and mixed effects models, and then takes the discussion beyond regression and analysis of variance to conclude. Pedagogically, the authors introduce theory and methodological basis topic by topic, present a problem as an application, followed by a SAS analysis of the data provided and a discussion of results. The text focuses on applied statistical problems and methods. Key features include: end of chapter exercises, downloadable SAS code and data sets, and advanced material suitable for a second course in applied statistics with every method explained using SAS analysis to illustrate a real-world problem. New to this edition: • Covers SAS v9.2 and incorporates new commands • Uses SAS ODS (output delivery system) for reproduction of tables and graphics output • Presents new commands needed to produce ODS output • All chapters rewritten for clarity • New and updated examples throughout • All SAS outputs are new and updated, including graphics • More exercises and problems • Completely new chapter on analysis of nonlinear and generalized linear models • Completely new appendix Mervyn G. Marasinghe, PhD, is Associate Professor Emeritus of Statistics at Iowa State University, where he has taught courses in statistical methods and statistical computing. Kenneth J. Koehler, PhD, is University Professor of Statistics at Iowa State University, where he teaches courses in statistical methodology at both graduate and undergraduate levels and primarily uses SAS to supplement his teaching.
This book brings together the voices of leading experts in the frontiers of biostatistics, biomedicine, and the health sciences to discuss the statistical procedures, useful methods, and novel applications in biostatistics research. It also includes discussions of potential future directions of biomedicine and new statistical developments for health research, with the intent of stimulating research and fostering the interactions of scholars across health research related disciplines. Topics covered include: Health data analysis and applications to EHR data Clinical trials, FDR, and applications in health science Big network analytics and its applications in GWAS Survival analysis and functional data analysis Graphical modelling in genomic studies The book will be valuable to data scientists and statisticians who are working in biomedicine and health, other practitioners in the health sciences, and graduate students and researchers in biostatistics and health.
Drawing on the work of internationally acclaimed experts in the field, Handbook of Item Response Theory, Volume Two: Statistical Tools presents classical and modern statistical tools used in item response theory (IRT). While IRT heavily depends on the use of statistical tools for handling its models and applications, systematic introductions and reviews that emphasize their relevance to IRT are hardly found in the statistical literature. This second volume in a three-volume set fills this void. Volume Two covers common probability distributions, the issue of models with both intentional and nuisance parameters, the use of information criteria, methods for dealing with missing data, and model identification issues. It also addresses recent developments in parameter estimation and model fit and comparison, such as Bayesian approaches, specifically Markov chain Monte Carlo (MCMC) methods.
Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.
In the concluding chapter of his famous book on the theory of evolution by natural selection, Charles Darwin (1859) remarked that: When the views entertained in this volume on the origin of species, or when analogous views are generally admitted, we can dimly foresee that there will be a considerable revolution in natural history. This proved, of course, to be completely correct. At present there is a great divergence of opinion about the general importance of natural selection in the evolutionary process. Nevertheless, biologists are, on the whole, united in their acceptance of the potential power of selection in changing populations. Given this situation, it is not surprising to find that many attempts to detect the effects of natural selection have been made since the time of Darwin. This area of study has been called ecological genetics. It involves the collection of data of various kinds and, in many cases, the development of special methods for analysing these data. This book is a summary of methods for data analysis, concentrating on those that are applicable to animal populations, particularly wild populations.
The definitive survey of computational intelligence from luminaries in the field Computational intelligence is a fast-moving, multidisciplinary field - the nexus of diverse technical interest areas that include neural networks, fuzzy logic, and evolutionary computation. Keeping up with computational intelligence means understanding how it relates to an ever-expanding range of applications. This is the book that ties it all together - and puts that understanding well within your reach. In Computational Intelligence: The Experts Speak, editors David B. Fogel and Charles J. Robinson present an unmatched compilation of expanded papers from plenary and special lecturers attending the 2002 IEEE World Congress on Computational Intelligence. Collectively, these papers provide a compelling snapshot of the issues that define the industry, as observed by some of the top minds in the computational intelligence community. In a series of topical chapters, this comprehensive volume shows how current technology is shaping computational intelligence, and it delivers eye-opening insights into the field's future challenges. The research detailed here covers an array of leading-edge applications, from coevolutionary robotics to underwater sensors and cognitive science, in such areas as: Self-organizing systems Situation awareness Human-machine interaction Automatic control Data recognition Computational Intelligence also includes introductions to each grouping of contributions that provide helpful tutorials and discuss important parallels between topics. Whatever your role might be in this dynamic, influential field, this is the one reference that no practitioner of computational intelligence should be without.
This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control and bilevel optimization. Recent developments concerning scalarization techniques, necessary and sufficient optimality conditions and duality statements are given. New numerical methods for efficiently solving set optimization problems are provided. Moreover, applications in economics, finance and risk theory are discussed. Summary The objective of this book is to present advances in different areas of variational analysis and set optimization, especially uncertain optimization, optimal control and bilevel optimization. Uncertain optimization problems will be approached from both a stochastic as well as a robust point of view. This leads to different interpretations of the solutions, which widens the choices for a decision-maker given his preferences. Recent developments regarding linear and nonlinear scalarization techniques with solid and nonsolid ordering cones for solving set optimization problems are discussed in this book. These results are useful for deriving optimality conditions for set and vector optimization problems. Consequently, necessary and sufficient optimality conditions are presented within this book, both in terms of scalarization as well as generalized derivatives. Moreover, an overview of existing duality statements and new duality assertions is given. The book also addresses the field of variable domination structures in vector and set optimization. Including variable ordering cones is especially important in applications such as medical image registration with uncertainties. This book covers a wide range of applications of set optimization. These range from finance, investment, insurance, control theory, economics to risk theory. As uncertain multi-objective optimization, especially robust approaches, lead to set optimization, one main focus of this book is uncertain optimization. Important recent developments concerning numerical methods for solving set optimization problems sufficiently fast are main features of this book. These are illustrated by various examples as well as easy-to-follow-steps in order to facilitate the decision process for users. Simple techniques aimed at practitioners working in the fields of mathematical programming, finance and portfolio selection are presented. These will help in the decision-making process, as well as give an overview of nondominated solutions to choose from.
This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.
It is our great pleasure to welcome you all to the 2002 AFSS International Conference on Fuzzy Systems (AFSS 2002) to be held in Calcutta, the great City of Joy. AFSS 2002 is the ?fth conference in the series initiated by the Asian Fuzzy Systems Society (AFSS). AFSS 2002 is jointly being organized by theIndianStatisticalInstitute(ISI)andJadavpurUniversity(JU). Likeprevious conferencesinthisseries,wearesure,AFSS2002willprovideaforumforfruitful interaction and exchange of ideas between the participants from all over the globe. The present conference covers all major facets of soft computing such as fuzzy logic, neural networks, genetic algorithms including both theories and applications. Wehopethismeetingwillbeenjoyableacademicallyandotherwise. We are thankful to the members of the International Program Committee and the Area Chairs for extending their support in various forms to make a strong technical program. Each submitted paper was reviewed by at least three referees, and in some cases the revised versions were again checked by the ref- ees. As a result of this tough screening process we could select only about 50% of the submitted papers. We again express our sincere thanks to all referees for doing a great job. We are happy to note that 19 di?erent countries from all over the globe are represented by the authors, thereby making it a truly inter- tional conference. We are proud to have a list of distinguished speakers including Profs. Z. Pawlak, J. Bezdek, D. Dubois, and T. Yamakawa.