Contributions To Linear Discriminant Analysis With Applications To Growth Curves
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Contributions To Linear Discriminant Analysis With Applications To Growth Curves
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Author : Edward Kanuti Ngailo
language : en
Publisher: Linköping University Electronic Press
Release Date : 2020-05-06
Contributions To Linear Discriminant Analysis With Applications To Growth Curves written by Edward Kanuti Ngailo and has been published by Linköping University Electronic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-06 with categories.
This thesis concerns contributions to linear discriminant analysis with applications to growth curves. Firstly, we present the linear discriminant function coefficients in a stochastic representation using random variables from the standard univariate distributions. We apply the characterized distribution in the classification function to approximate the classification error rate. The results are then extended to large dimension asymptotics under assumption that the dimension p of the parameter space increases together with the sample size n to infinity such that the ratio converges to a positive constant c (0, 1). Secondly, the thesis treats repeated measures data which correspond to multiple measurements that are taken on the same subject at different time points. We develop a linear classification function to classify an individual into one out of two populations on the basis of the repeated measures data that when the means follow a growth curve structure. The growth curve structure we first consider assumes that all treatments (groups) follows the same growth profile. However, this is not necessarily true in general and the problem is extended to linear classification where the means follow an extended growth curve structure, i.e., the treatments under the experimental design follow different growth profiles. At last, a function of the inverse Wishart matrix and a normal distribution finds its application in portfolio theory where the vector of optimal portfolio weights is proportional to the product of the inverse sample covariance matrix and a sample mean vector. Analytical expressions for higher order moments and non-central moments of the portfolio weights are derived when the returns are assumed to be independently multivariate normally distributed. Moreover, the expressions for the mean, variance, skewness and kurtosis of specific estimated weights are obtained. The results are complemented using a Monte Carlo simulation study, where data from the multivariate normal and t-distributions are discussed. Den här avhandlingen studerar diskriminantanalys, klassificering av tillväxtkurvor och portföljteori. Diskriminantanalys och klassificering är flerdimensionella tekniker som används för att separera olika mängder av objekt och för att tilldela nya objekt till redan definierade grupper (så kallade klasser). En klassisk metod är att använda Fishers linjära diskriminantfunktion och när alla parametrar är kända så kan man enkelt beräkna sannolikheterna för felklassificering. Tyvärr är så sällan fallet, utan parametrarna måste skattas från data, och då blir Fishers linjära diskriminantfunktion en funktion av en Wishartmatris och multivariat normalfördelade vektorer. I den här avhandlingen studerar vi hur man kan approximativt beräkna sannolikheten för felklassificering under antagande att dimensionen på parameterrummet ökar tillsammans med antalet observationer genom att använda en särskild stokastisk representation av diskriminantfunktionen. Upprepade mätningar över tiden på samma individ eller objekt går att modellera med så kallade tillväxtkurvor. Vid klassificering av tillväxtkurvor, eller rättare sagt av upprepade mätningar för en ny individ, bör man ta tillvara på både den spatiala- och temporala informationen som finns hos dessa observationer. Vi vidareutvecklar Fishers linjära diskriminantfunktion att passa för upprepade mätningar och beräknar asymptotiska sannolikheter för felklassificering. Till sist kan man notera att snarlika funktioner av Wishartmatriser och multivariat normalfördelade vektorer dyker upp när man vill beräkna de optimala vikterna i portföljteori. Genom en stokastisk representation studerar vi egenskaperna hos portföljvikterna och gör dessutom en simuleringsstudie för att förstå vad som händer när antagandet om normalfördelning inte är uppfyllt.
Applied Univariate Bivariate And Multivariate Statistics
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Author : Daniel J. Denis
language : en
Publisher: John Wiley & Sons
Release Date : 2021-04-13
Applied Univariate Bivariate And Multivariate Statistics written by Daniel J. Denis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-13 with Mathematics categories.
AN UPDATED GUIDE TO STATISTICAL MODELING TECHNIQUES USED IN THE SOCIAL AND NATURAL SCIENCES This revised and updated second edition of Applied Univariate, Bivariate, and Multivariate Statistics: Understanding Statistics for Social and Natural Scientists, with Applications in SPSS and R contains an accessible introduction to statistical modeling techniques commonly used in the social and natural sciences. The text offers a blend of statistical theory and methodology and reviews both the technical and theoretical aspects of good data analysis. Featuring applied resources at various levels, the book includes statistical techniques using software packages such as R and SPSS®. To promote a more in-depth interpretation of statistical techniques across the sciences, the book surveys some of the technical arguments underlying formulas and equations. The second edition has been designed to be more approachable by minimizing theoretical or technical jargon and maximizing conceptual understanding with easy-to-apply software examples. This important text: Offers demonstrations of statistical techniques using software packages such as R and SPSS® Contains examples of hypothetical and real data with statistical analyses Provides historical and philosophical insights into many of the techniques used in modern science Includes a companion website that features further instructional details, additional data sets, and solutions to selected exercises Written for students of social and applied sciences, Applied Univariate, Bivariate, and Multivariate Statistics, Second Edition offers a thorough introduction to the world of statistical modeling techniques in the sciences.
Current Index To Journals In Education
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Author :
language : en
Publisher:
Release Date : 1998
Current Index To Journals In Education written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Education categories.
Stock Identification Methods
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Author : Lisa A. Kerr
language : en
Publisher: Elsevier
Release Date : 2004-10-15
Stock Identification Methods written by Lisa A. Kerr and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-15 with Technology & Engineering categories.
Stock Identification Methods provides a comprehensive review of the various disciplines used to study the population structure of fishery resources. It represents the worldwide experience and perspectives of experts on each method, assembled through a working group of the International Council for the Exploration of the Sea. The book is organized to foster interdisciplinary analyses and conclusions about stock structure, a crucial topic for fishery science and management. Technological advances have promoted the development of stock identification methods in many directions, resulting in a confusing variety of approaches. Based on central tenets of population biology and management needs, Stock Identification Methods offers a unified framework for understanding stock structure by promoting an understanding of the relative merits and sensitivities of each approach.* Describes eighteen distinct approaches to stock identification grouped into sections on life history traits, environmental signals, genetic analyses, and applied marks* Features experts' reviews of benchmark case studies, general protocols, and the strengths and weaknesses of each identification method* Reviews statistical techniques for exploring stock patterns, testing for differences among putative stocks, stock discrimination, and stock composition analysis* Focuses on the challenges of interpreting data and managing mixed-stock fisheries
Methods Of Multivariate Analysis
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Author : Alvin C. Rencher
language : en
Publisher: John Wiley & Sons
Release Date : 2012-07-10
Methods Of Multivariate Analysis written by Alvin C. Rencher and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-10 with Mathematics categories.
Praise for the Second Edition "This book is a systematic, well-written, well-organized text on multivariate analysis packed with intuition and insight . . . There is much practical wisdom in this book that is hard to find elsewhere." IIE Transactions Filled with new and timely content, Methods of Multivariate Analysis, Third Edition provides examples and exercises based on more than sixty real data sets from a wide variety of scientific fields. It takes a "methods" approach to the subject, placing an emphasis on how students and practitioners can employ multivariate analysis in real-life situations. This Third Edition continues to explore the key descriptive and inferential procedures that result from multivariate analysis. Following a brief overview of the topic, the book goes on to review the fundamentals of matrix algebra, sampling from multivariate populations, and the extension of common univariate statistical procedures (including t-tests, analysis of variance, and multiple regression) to analogous multivariate techniques that involve several dependent variables. The latter half of the book describes statistical tools that are uniquely multivariate in nature, including procedures for discriminating among groups, characterizing low-dimensional latent structure in high-dimensional data, identifying clusters in data, and graphically illustrating relationships in low-dimensional space. In addition, the authors explore a wealth of newly added topics, including: Confirmatory Factor Analysis Classification Trees Dynamic Graphics Transformations to Normality Prediction for Multivariate Multiple Regression Kronecker Products and Vec Notation New exercises have been added throughout the book, allowing readers to test their comprehension of the presented material. Detailed appendices provide partial solutions as well as supplemental tables, and an accompanying FTP site features the book's data sets and related SAS® code. Requiring only a basic background in statistics, Methods of Multivariate Analysis, Third Edition is an excellent book for courses on multivariate analysis and applied statistics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for both statisticians and researchers across a wide variety of disciplines.
Applied Multivariate Analysis
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Author : Neil H. Timm
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-21
Applied Multivariate Analysis written by Neil H. Timm and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-21 with Mathematics categories.
Univariate statistical analysis is concerned with techniques for the analysis of a single random variable. This book is about applied multivariate analysis. It was written to p- vide students and researchers with an introduction to statistical techniques for the ana- sis of continuous quantitative measurements on several random variables simultaneously. While quantitative measurements may be obtained from any population, the material in this text is primarily concerned with techniques useful for the analysis of continuous obser- tions from multivariate normal populations with linear structure. While several multivariate methods are extensions of univariate procedures, a unique feature of multivariate data an- ysis techniques is their ability to control experimental error at an exact nominal level and to provide information on the covariance structure of the data. These features tend to enhance statistical inference, making multivariate data analysis superior to univariate analysis. While in a previous edition of my textbook on multivariate analysis, I tried to precede a multivariate method with a corresponding univariate procedure when applicable, I have not taken this approach here. Instead, it is assumed that the reader has taken basic courses in multiple linear regression, analysis of variance, and experimental design. While students may be familiar with vector spaces and matrices, important results essential to multivariate analysis are reviewed in Chapter 2. I have avoided the use of calculus in this text.
Big Data Analytics For Smart Healthcare Applications
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Author : Celestine Iwendi
language : en
Publisher: Frontiers Media SA
Release Date : 2023-04-17
Big Data Analytics For Smart Healthcare Applications written by Celestine Iwendi and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-17 with Medical categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2004
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Multivariate Reduced Rank Regression
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Author : Gregory C. Reinsel
language : en
Publisher: Springer Nature
Release Date : 2022-11-30
Multivariate Reduced Rank Regression written by Gregory C. Reinsel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-30 with Mathematics categories.
This book provides an account of multivariate reduced-rank regression, a tool of multivariate analysis that enjoys a broad array of applications. In addition to a historical review of the topic, its connection to other widely used statistical methods, such as multivariate analysis of variance (MANOVA), discriminant analysis, principal components, canonical correlation analysis, and errors-in-variables models, is also discussed. This new edition incorporates Big Data methodology and its applications, as well as high-dimensional reduced-rank regression, generalized reduced-rank regression with complex data, and sparse and low-rank regression methods. Each chapter contains developments of basic theoretical results, as well as details on computational procedures, illustrated with numerical examples drawn from disciplines such as biochemistry, genetics, marketing, and finance. This book is designed for advanced students, practitioners, and researchers, who may deal with moderate and high-dimensional multivariate data. Because regression is one of the most popular statistical methods, the multivariate regression analysis tools described should provide a natural way of looking at large (both cross-sectional and chronological) data sets. This book can be assigned in seminar-type courses taken by advanced graduate students in statistics, machine learning, econometrics, business, and engineering.
Methods Of Multivariate Analysis Basic Applications
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Author : Alvin C. Rencher
language : en
Publisher: Wiley-Interscience
Release Date : 1995-02-20
Methods Of Multivariate Analysis Basic Applications written by Alvin C. Rencher and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-02-20 with Mathematics categories.
The accompanying diskette contains all of the data sets and SAS command files for all of the examples. (SAS is the leading statistical computer package on the market.) Students can adapt these command files to work problems in the text.