Kupper / Neelon / O'Brien Exercises and Solutions in Biostatistical Theory

1. Auflage 2010
ISBN: 978-1-4398-9502-3
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 420 Seiten

Reihe: Chapman & Hall/CRC Texts in Statistical Science

Drawn from nearly four decades of Lawrence L. Kupper’s teaching experiences as a distinguished professor in the Department of Biostatistics at the University of North Carolina, Exercises and Solutions in Biostatistical Theory presents theoretical statistical concepts, numerous exercises, and detailed solutions that span topics from basic probability to statistical inference. The text links theoretical biostatistical principles to real-world situations, including some of the authors’ own biostatistical work that has addressed complicated design and analysis issues in the health sciences.

This classroom-tested material is arranged sequentially starting with a chapter on basic probability theory, followed by chapters on univariate distribution theory and multivariate distribution theory. The last two chapters on statistical inference cover estimation theory and hypothesis testing theory. Each chapter begins with an in-depth introduction that summarizes the biostatistical principles needed to help solve the exercises. Exercises range in level of difficulty from fairly basic to more challenging (identified with asterisks).

By working through the exercises and detailed solutions in this book, students will develop a deep understanding of the principles of biostatistical theory. The text shows how the biostatistical theory is effectively used to address important biostatistical issues in a variety of real-world settings. Mastering the theoretical biostatistical principles described in the book will prepare students for successful study of higher-level statistical theory and will help them become better biostatisticians.

Autoren/Hrsg.

Kupper, Lawrence

Neelon, Brian

O'Brien, Sean M.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Basic Probability Theory
Counting Formulas (N-tuples, permutations, combinations, Pascal’s identity, Vandermonde’s identity)
Probability Formulas (union, intersection, complement, mutually exclusive events, conditional probability, independence, partitions, Bayes’ theorem)

Univariate Distribution Theory
Discrete and Continuous Random Variables
Cumulative Distribution Functions
Median and Mode
Expectation Theory
Some Important Expectations (mean, variance, moments, moment generating function, probability generating function)
Inequalities Involving Expectations
Some Important Probability Distributions for Discrete Random Variables
Some Important Distributions (i.e., Density Functions) for Continuous Random Variables

Multivariate Distribution Theory
Discrete and Continuous Multivariate Distributions
Multivariate Cumulative Distribution Functions
Expectation Theory (covariance, correlation, moment generating function)
Marginal Distributions
Conditional Distributions and Expectations
Mutual Independence among a Set of Random Variables
Random Sample
Some Important Multivariate Discrete and Continuous Probability Distributions
Special Topics of Interest (mean and variance of a linear function, convergence in distribution and the Central Limit Theorem, order statistics, transformations)

Estimation Theory
Point Estimation of Population Parameters (method of moments, unweighted and weighted least squares, maximum likelihood)
Data Reduction and Joint Sufficiency (Factorization Theorem)
Methods for Evaluating the Properties of a Point Estimator (mean-squared error, Cramér–Rao lower bound, efficiency, completeness, Rao–Blackwell theorem)
Interval Estimation of Population Parameters (normal distribution-based exact intervals, Slutsky’s theorem, consistency, maximum-likelihood-based approximate intervals)

Hypothesis Testing Theory
Basic Principles (simple and composite hypotheses, null and alternative hypotheses, Type I and Type II errors, power, P-value)
Most Powerful (MP) and Uniformly Most Powerful (UMP) Tests (Neyman–Pearson Lemma)
Large-Sample ML-Based Methods for Testing a Simple Null Hypothesis versus a Composite Alternative Hypothesis (likelihood ratio, Wald, and score tests)
Large-Sample ML-Based Methods for Testing a Composite Null Hypothesis versus a Composite Alternative Hypothesis (likelihood ratio, Wald, and score tests)

Appendix: Useful Mathematical Results

References

Index

Exercises and Solutions appear at the end of each chapter.