matrix algebra theory computations and applications in statistics springer texts in statistics

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Matrix Algebra

Author : James E. Gentle
ISBN : 9783319648675
Genre : Mathematics
File Size : 46. 96 MB
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Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

Information Criteria And Statistical Modeling

Author : Sadanori Konishi
ISBN : 0387718877
Genre : Mathematics
File Size : 85. 39 MB
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Statistical modeling is a critical tool in scientific research. This book provides comprehensive explanations of the concepts and philosophy of statistical modeling, together with a wide range of practical and numerical examples. The authors expect this work to be of great value not just to statisticians but also to researchers and practitioners in various fields of research such as information science, computer science, engineering, bioinformatics, economics, marketing and environmental science. It’s a crucial area of study, as statistical models are used to understand phenomena with uncertainty and to determine the structure of complex systems. They’re also used to control such systems, as well as to make reliable predictions in various natural and social science fields.

Statistics For Earth And Environmental Scientists

Author : John Schuenemeyer
ISBN : 9781118102213
Genre : Mathematics
File Size : 32. 87 MB
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A comprehensive treatment of statistical applications for solving real-world environmental problems A host of complex problems face today's earth science community, such as evaluating the supply of remaining non-renewable energy resources, assessing the impact of people on the environment, understanding climate change, and managing the use of water. Proper collection and analysis of data using statistical techniques contributes significantly toward the solution of these problems. Statistics for Earth and Environmental Scientists presents important statistical concepts through data analytic tools and shows readers how to apply them to real-world problems. The authors present several different statistical approaches to the environmental sciences, including Bayesian and nonparametric methodologies. The book begins with an introduction to types of data, evaluation of data, modeling and estimation, random variation, and sampling—all of which are explored through case studies that use real data from earth science applications. Subsequent chapters focus on principles of modeling and the key methods and techniques for analyzing scientific data, including: Interval estimation and Methods for analyzinghypothesis testing of means time series data Spatial statistics Multivariate analysis Discrete distributions Experimental design Most statistical models are introduced by concept and application, given as equations, and then accompanied by heuristic justification rather than a formal proof. Data analysis, model building, and statistical inference are stressed throughout, and readers are encouraged to collect their own data to incorporate into the exercises at the end of each chapter. Most data sets, graphs, and analyses are computed using R, but can be worked with using any statistical computing software. A related website features additional data sets, answers to selected exercises, and R code for the book's examples. Statistics for Earth and Environmental Scientists is an excellent book for courses on quantitative methods in geology, geography, natural resources, and environmental sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for earth scientists, geologists, hydrologists, and environmental statisticians who collect and analyze data in their everyday work.

Journal Of The American Statistical Association

Author :
ISBN : UOM:39015072641353
Genre : Statistics
File Size : 43. 99 MB
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Modern Multivariate Statistical Techniques

Author : Alan J. Izenman
ISBN : 0387781897
Genre : Mathematics
File Size : 73. 20 MB
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This is the first book on multivariate analysis to look at large data sets which describes the state of the art in analyzing such data. Material such as database management systems is included that has never appeared in statistics books before.

Numerical Analysis For Statisticians

Author : Kenneth Lange
ISBN : 0387949798
Genre : Mathematics
File Size : 36. 58 MB
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This text presents topics in numerical analysis for statisticians. It would be suitable as a text for a graduate course in statistical computing. The focus is on principles of numerical analysis intended to equip students to craft their own software and to understand the advantages and disadvantages of different numerical methods.

Amstat News

Author :
ISBN : UOM:39015059069131
Genre : Statistics
File Size : 90. 73 MB
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A Sas Iml Companion For Linear Models

Author : Jamis J. Perrett
ISBN : 9781441955562
Genre : Mathematics
File Size : 48. 78 MB
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Linear models courses are often presented as either theoretical or applied. Consequently, students may find themselves either proving theorems or using high-level procedures like PROC GLM to analyze data. There exists a gap between the derivation of formulas and analyses that hide these formulas behind attractive user interfaces. This book bridges that gap, demonstrating theory put into practice. Concepts presented in a theoretical linear models course are often trivialized in applied linear models courses by the facility of high-level SAS procedures like PROC MIXED and PROC REG that require the user to provide a few options and statements and in return produce vast amounts of output. This book uses PROC IML to show how analytic linear models formulas can be typed directly into PROC IML, as they were presented in the linear models course, and solved using data. This helps students see the link between theory and application. This also assists researchers in developing new methodologies in the area of linear models. The book contains complete examples of SAS code for many of the computations relevant to a linear models course. However, the SAS code in these examples automates the analytic formulas. The code for high-level procedures like PROC MIXED is also included for side-by-side comparison. The book computes basic descriptive statistics, matrix algebra, matrix decomposition, likelihood maximization, non-linear optimization, etc. in a format conducive to a linear models or a special topics course. Also included in the book is an example of a basic analysis of a linear mixed model using restricted maximum likelihood estimation (REML). The example demonstrates tests for fixed effects, estimates of linear functions, and contrasts. The example starts by showing the steps for analyzing the data using PROC IML and then provides the analysis using PROC MIXED. This allows students to follow the process that lead to the output.

Numerical Analysis

Author : Walter Gautschi
ISBN : 0817638954
Genre : Mathematics
File Size : 85. 37 MB
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'The book reads like an unfolding story... Topics are motivated with great care and ingenuity that might be given to establishing the drive behind characters in a good novel... Clarity is never sacrificed for elegance. Above all, the pace is always lively

Representation Theory Of Finite Groups

Author : Benjamin Steinberg
ISBN : 1461407761
Genre : Mathematics
File Size : 36. 24 MB
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This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.

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