Mathematical Statistics: An Introduction to Likelihood Based Inference – eBook

Description

Discover a comprehensive exploration of mathematical statistics with the ebook, **Mathematical Statistics: An Introduction to Likelihood Based Inference (PDF)**. This essential textbook provides a cohesive understanding of fundamental statistical concepts such as parametric estimation, hypothesis testing, confidence intervals, and statistical modeling—all anchored around the pivotal likelihood function. Catering specifically to first-year graduate students and advanced undergraduates, this text unifies key topics to foster a deeper grasp of statistical inference.

In **Mathematical Statistics: An Introduction to Likelihood Based Inference**, author Rossi presents a fresh perspective on mathematical statistics, advancing beyond typical textbooks by delving into intricate concepts with clarity and depth. Chapters seamlessly connect various topics, emphasizing the critical aspects of statistical modeling, including exponential family distributions, sufficiency, and large sample properties. This resource not only simplifies advanced topics but also provides a thorough examination, making it an indispensable tool for anyone serious about mastering statistical inference.

The textbook thoroughly covers likelihood-based estimation, paying particular attention to multidimensional parameter spaces and range-dependent support. A dedicated chapter on confidence intervals includes in-depth discussions on exact confidence intervals as well as standard large sample confidence intervals based on Maximum Likelihood Estimates (MLEs) and bootstrap methods. Furthermore, it features a segment on parametric statistical models, incorporating insights on Poisson regression, non-independent and identically distributed (non-iid) observations, logistic regression, and linear regression techniques.

– Engaging with practical problems, this book features a variety of examples ranging from introductory exercises to challenging problems, equipped with thorough solutions.
– It offers insightful sections on Bayesian estimation and credible intervals, broadening the reader’s understanding of modern statistical methodologies.
– The material prepares students for future endeavors in statistics and data science by equipping them with essential tools and concepts.
– Attention is also directed towards important concepts in statistical modeling, including exponential family distribution, sufficiency, and large sample properties.
– Captivating case studies draw on **real-life data** from events such as the Donner party tragedy, Yellowstone National Park observations, and the Titanic voyage, providing context and practical applications.

**Mathematical Statistics: An Introduction to Likelihood Based Inference** stands as a premier textbook for graduate and upper-undergraduate courses focused on mathematical statistics, probability, and statistical inference. This ebook will be invaluable for learners aiming to excel in their statistical studies and apply their knowledge in data-driven fields.

ISBN: 978-XXXX-XXXX-1, 978-XXXX-XXXX-2, 978-XXXX-XXXX-3.