Download or read book Contributions to linear discriminant analysis with applications to growth curves written by Edward Kanuti Ngailo and published by Linköping University Electronic Press. This book was released on 2020-05-06 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Discriminant Analysis and Applications written by T. Cacoullos and published by Academic Press. This book was released on 2014-05-10 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discriminant Analysis and Applications comprises the proceedings of the NATO Advanced Study Institute on Discriminant Analysis and Applications held in Kifissia, Athens, Greece in June 1972. The book presents the theory and applications of Discriminant analysis, one of the most important areas of multivariate statistical analysis. This volume contains chapters that cover the historical development of discriminant analysis methods; logistic and quasi-linear discrimination; and distance functions. Medical and biological applications, and computer graphical analysis and graphical techniques for multidimensional data are likewise discussed. Statisticians, mathematicians, and biomathematicians will find the book very interesting.
Download or read book Contributions to Discriminant Analysis of Cross sectional and Longitudinal Data with Applications written by Alice M. Hinton and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: There are a variety of methods available to classify an object into one of two populations. Here, the method of discriminant analysis is considered in the cross-sectional and the longitudinal setting with a structured multivariate normal model. The generalized likelihood ratio change detection algorithm is also investigated as an alternative to methods based on discriminant analysis in the longitudinal setting. Traditionally, discriminant functions are developed to classify a new observation from a cross-sectional dataset into a population. An error is made when the observation is incorrectly classified. In the literature, several parametric and empirical methods of estimating these misclassification probabilities have been proposed. The performance of six parametric and three empirical misclassification probability estimators are compared. It is found that the parametric methods, which rely on an assumption of normality, generally outperform the empirical methods when a linear discriminant function is used for classification and the data originate from normal populations. The preferred parametric method depends on the size of the training dataset and the parameters of the populations, particularly the distance between the means. The empirical methods are preferred only when the two populations are well separated and the variances are significantly different.
Download or read book Discriminant Analysis written by William R. Klecka and published by SAGE Publications, Incorporated. This book was released on 1980-08-01 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: These procedures, collectively known as discriminant analysis, allow a researcher to study the difference between two or more groups of objects with respect to several variables simultaneously, determining whether meaningful differences exist between the groups and identifying the discriminating power of each variable.
Download or read book Discriminant Analysis written by Peter A. Lachenbruch and published by . This book was released on 1975 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic ideas of discriminant analysis; Evaluating a discriminant function; Robustness of the linear discriminant function; Nonnormal and nonparametric methods; Multiple-group problems; Miscellaneous problems.
Download or read book Discrete Discriminant Analysis written by Matthew Goldstein and published by John Wiley & Sons. This book was released on 1978 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The linear discriminant function; Discrete classification models; Error rates and the problem of bias; The variable-selection problem; Special topics; Computer programs.
Download or read book Applied Univariate Bivariate and Multivariate Statistics written by Daniel J. Denis and published by John Wiley & Sons. This book was released on 2021-04-01 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stock Identification Methods written by Lisa A. Kerr and published by Elsevier. This book was released on 2004-10-15 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1852 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methodology and Applications of Statistics written by Barry C. Arnold and published by Springer Nature. This book was released on 2022-01-04 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to one of the most outstanding researchers in the field of statistics, this volume in honor of C.R. Rao, on the occasion of his 100th birthday, provides a bird’s-eye view of a broad spectrum of research topics, paralleling C.R. Rao’s wide-ranging research interests. The book’s contributors comprise a representative sample of the countless number of researchers whose careers have been influenced by C.R. Rao, through his work or his personal aid and advice. As such, written by experts from more than 15 countries, the book’s original and review contributions address topics including statistical inference, distribution theory, estimation theory, multivariate analysis, hypothesis testing, statistical modeling, design and sampling, shape and circular analysis, and applications. The book will appeal to statistics researchers, theoretical and applied alike, and PhD students. Happy Birthday, C.R. Rao!
Download or read book Current Index to Journals in Education written by and published by . This book was released on 1998-04 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods of Multivariate Analysis Basic Applications written by Alvin C. Rencher and published by Wiley-Interscience. This book was released on 1995-02-20 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applied Multivariate Analysis written by Neil H. Timm and published by Springer Science & Business Media. This book was released on 2002-06-19 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad overview of the basic theory and methods of applied multivariate analysis. The presentation integrates both theory and practice including both the analysis of formal linear multivariate models and exploratory data analysis techniques. Each chapter contains the development of basic theoretical results with numerous applications illustrated using examples from the social and behavioral sciences, and other disciplines. All examples are analyzed using SAS for Windows Version 8.0.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1987 with total page 1390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Download or read book Multivariate Reduced Rank Regression written by Gregory C. Reinsel and published by Springer Nature. This book was released on 2022-11-30 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Reviewer s Guide to Quantitative Methods in the Social Sciences written by Gregory R. Hancock and published by Routledge. This book was released on 2010-04-26 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for reviewers of research manuscripts and proposals in the social and behavioral sciences, and beyond, this title includes chapters that address traditional and emerging quantitative methods of data analysis.
Download or read book Management written by and published by . This book was released on 1978 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
