Biased Estimators in the Linear Regression Model PDF Download

Author: Götz Trenkler
Publisher:
ISBN: 9780899460727
Category : Econometrics
Languages : en
Pages : 163

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Author: Andrew W. Bruce
Publisher: Springer Science & Business Media
ISBN: 1447113985
Category : Medical
Languages : en
Pages : 363

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Book Description
Carcinoma of the prostate increasingly dominates the attention of urologists for both scientific and clinical reasons. The search for an explanation and the prediction of the variable behaviour of the malignant prostatic cell continues unabated. The search for more precise tumour staging and more effective treatment is equally vigorous. Editors Andrew Bruce and John Trachtenberg have assembled acknowledged leaders in prostate cancer to present those areas of direct interest to the clinician. There are a number of other topics that might have been considered but most of these, such as experimental tumour models or biochemical factors affecting cell growth, still lack immediate application for the clinician. Carcinoma of the prostate continues to have its highest incidence in the western world, and the difference in comparison with the incidence in the Far East appears to be real and not masked by diagnostic or other factors. A number of other epidemiological aspects need careful analysis: Is the incidence increasing? Is the survival improving? Is the prognosis worse in the younger patient? Epidemiological data are easily misused and misinterpreted so that a precise analysis of the known facts makes an important opening chapter to this book.

Author: Arthur Stanley Goldberger
Publisher: Harvard University Press
ISBN: 9780674175440
Category : Business & Economics
Languages : en
Pages : 430

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This text prepares first-year graduate students and advanced undergraduates for empirical research in economics, and also equips them for specialization in econometric theory, business, and sociology. A Course in Econometrics is likely to be the text most thoroughly attuned to the needs of your students. Derived from the course taught by Arthur S. Goldberger at the University of Wisconsin-Madison and at Stanford University, it is specifically designed for use over two semesters, offers students the most thorough grounding in introductory statistical inference, and offers a substantial amount of interpretive material. The text brims with insights, strikes a balance between rigor and intuition, and provokes students to form their own critical opinions. A Course in Econometrics thoroughly covers the fundamentals--classical regression and simultaneous equations--and offers clear and logical explorations of asymptotic theory and nonlinear regression. To accommodate students with various levels of preparation, the text opens with a thorough review of statistical concepts and methods, then proceeds to the regression model and its variants. Bold subheadings introduce and highlight key concepts throughout each chapter. Each chapter concludes with a set of exercises specifically designed to reinforce and extend the material covered. Many of the exercises include real microdata analyses, and all are ideally suited to use as homework and test questions.

Author: Marvin H. J. Gruber
Publisher: JHU Press
ISBN: 0801894263
Category : Mathematics
Languages : en
Pages : 425

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Praise for the first edition --

Author: Jürgen Groß
Publisher: Springer Science & Business Media
ISBN: 364255864X
Category : Mathematics
Languages : en
Pages : 400

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Book Description
The book covers the basic theory of linear regression models and presents a comprehensive survey of different estimation techniques as alternatives and complements to least squares estimation. Proofs are given for the most relevant results, and the presented methods are illustrated with the help of numerical examples and graphics. Special emphasis is placed on practicability and possible applications. The book is rounded off by an introduction to the basics of decision theory and an appendix on matrix algebra.

Author: A. K. Md. Ehsanes Saleh
Publisher: John Wiley & Sons
ISBN: 1118644506
Category : Mathematics
Languages : en
Pages : 404

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A guide to the systematic analytical results for ridge, LASSO, preliminary test, and Stein-type estimators with applications Theory of Ridge Regression Estimation with Applications offers a comprehensive guide to the theory and methods of estimation. Ridge regression and LASSO are at the center of all penalty estimators in a range of standard models that are used in many applied statistical analyses. Written by noted experts in the field, the book contains a thorough introduction to penalty and shrinkage estimation and explores the role that ridge, LASSO, and logistic regression play in the computer intensive area of neural network and big data analysis. Designed to be accessible, the book presents detailed coverage of the basic terminology related to various models such as the location and simple linear models, normal and rank theory-based ridge, LASSO, preliminary test and Stein-type estimators. The authors also include problem sets to enhance learning. This book is a volume in the Wiley Series in Probability and Statistics series that provides essential and invaluable reading for all statisticians. This important resource: Offers theoretical coverage and computer-intensive applications of the procedures presented Contains solutions and alternate methods for prediction accuracy and selecting model procedures Presents the first book to focus on ridge regression and unifies past research with current methodology Uses R throughout the text and includes a companion website containing convenient data sets Written for graduate students, practitioners, and researchers in various fields of science, Theory of Ridge Regression Estimation with Applications is an authoritative guide to the theory and methodology of statistical estimation.

Author: Marco Taboga
Publisher: Createspace Independent Publishing Platform
ISBN: 9781981369195
Category : Mathematical statistics
Languages : en
Pages : 670

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Book Description
The book is a collection of 80 short and self-contained lectures covering most of the topics that are usually taught in intermediate courses in probability theory and mathematical statistics. There are hundreds of examples, solved exercises and detailed derivations of important results. The step-by-step approach makes the book easy to understand and ideal for self-study. One of the main aims of the book is to be a time saver: it contains several results and proofs, especially on probability distributions, that are hard to find in standard references and are scattered here and there in more specialistic books. The topics covered by the book are as follows. PART 1 - MATHEMATICAL TOOLS: set theory, permutations, combinations, partitions, sequences and limits, review of differentiation and integration rules, the Gamma and Beta functions. PART 2 - FUNDAMENTALS OF PROBABILITY: events, probability, independence, conditional probability, Bayes' rule, random variables and random vectors, expected value, variance, covariance, correlation, covariance matrix, conditional distributions and conditional expectation, independent variables, indicator functions. PART 3 - ADDITIONAL TOPICS IN PROBABILITY THEORY: probabilistic inequalities, construction of probability distributions, transformations of probability distributions, moments and cross-moments, moment generating functions, characteristic functions. PART 4 - PROBABILITY DISTRIBUTIONS: Bernoulli, binomial, Poisson, uniform, exponential, normal, Chi-square, Gamma, Student's t, F, multinomial, multivariate normal, multivariate Student's t, Wishart. PART 5 - MORE DETAILS ABOUT THE NORMAL DISTRIBUTION: linear combinations, quadratic forms, partitions. PART 6 - ASYMPTOTIC THEORY: sequences of random vectors and random variables, pointwise convergence, almost sure convergence, convergence in probability, mean-square convergence, convergence in distribution, relations between modes of convergence, Laws of Large Numbers, Central Limit Theorems, Continuous Mapping Theorem, Slutsky's Theorem. PART 7 - FUNDAMENTALS OF STATISTICS: statistical inference, point estimation, set estimation, hypothesis testing, statistical inferences about the mean, statistical inferences about the variance.

Author: Douglas C. Montgomery
Publisher: John Wiley & Sons
ISBN: 1119180171
Category : Mathematics
Languages : en
Pages : 679

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Praise for the Fourth Edition "As with previous editions, the authors have produced a leading textbook on regression." —Journal of the American Statistical Association A comprehensive and up-to-date introduction to the fundamentals of regression analysis Introduction to Linear Regression Analysis, Fifth Edition continues to present both the conventional and less common uses of linear regression in today’s cutting-edge scientific research. The authors blend both theory and application to equip readers with an understanding of the basic principles needed to apply regression model-building techniques in various fields of study, including engineering, management, and the health sciences. Following a general introduction to regression modeling, including typical applications, a host of technical tools are outlined such as basic inference procedures, introductory aspects of model adequacy checking, and polynomial regression models and their variations. The book then discusses how transformations and weighted least squares can be used to resolve problems of model inadequacy and also how to deal with influential observations. The Fifth Edition features numerous newly added topics, including: A chapter on regression analysis of time series data that presents the Durbin-Watson test and other techniques for detecting autocorrelation as well as parameter estimation in time series regression models Regression models with random effects in addition to a discussion on subsampling and the importance of the mixed model Tests on individual regression coefficients and subsets of coefficients Examples of current uses of simple linear regression models and the use of multiple regression models for understanding patient satisfaction data. In addition to Minitab, SAS, and S-PLUS, the authors have incorporated JMP and the freely available R software to illustrate the discussed techniques and procedures in this new edition. Numerous exercises have been added throughout, allowing readers to test their understanding of the material. Introduction to Linear Regression Analysis, Fifth Edition is an excellent book for statistics and engineering courses on regression at the upper-undergraduate and graduate levels. The book also serves as a valuable, robust resource for professionals in the fields of engineering, life and biological sciences, and the social sciences.

Author: Bernhard Schipp
Publisher: Springer Science & Business Media
ISBN: 3790821217
Category : Mathematics
Languages : en
Pages : 438

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Book Description
This Festschrift is dedicated to Götz Trenkler on the occasion of his 65th birthday. As can be seen from the long list of contributions, Götz has had and still has an enormous range of interests, and colleagues to share these interests with. He is a leading expert in linear models with a particular focus on matrix algebra in its relation to statistics. He has published in almost all major statistics and matrix theory journals. His research activities also include other areas (like nonparametrics, statistics and sports, combination of forecasts and magic squares, just to mention afew). Götz Trenkler was born in Dresden in 1943. After his school years in East G- many and West-Berlin, he obtained a Diploma in Mathematics from Free University of Berlin (1970), where he also discovered his interest in Mathematical Statistics. In 1973, he completed his Ph.D. with a thesis titled: On a distance-generating fu- tion of probability measures. He then moved on to the University of Hannover to become Lecturer and to write a habilitation-thesis (submitted 1979) on alternatives to the Ordinary Least Squares estimator in the Linear Regression Model, a topic that would become his predominant ?eld of research in the years to come.

Author: C.Radhakrishna Rao
Publisher: Springer Science & Business Media
ISBN: 1489900241
Category : Mathematics
Languages : en
Pages : 360

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Book Description
The book is based on both authors' several years of experience in teaching linear models at various levels. It gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and offers a selection of classical and modern algebraic results that are useful in research work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results about the definiteness of matrices, especially for the differences of matrices, which enable superiority comparisons of two biased estimates to be made for the first time. We have attempted to provide a unified theory of inference from linear models with minimal assumptions. Besides the usual least-squares theory, alternative methods of estimation and testing based on convex loss func tions and general estimating equations are discussed. Special emphasis is given to sensitivity analysis and model selection. A special chapter is devoted to the analysis of categorical data based on logit, loglinear, and logistic regression models. The material covered, theoretical discussion, and its practical applica tions will be useful not only to students but also to researchers and con sultants in statistics.