Mathematical Statistics

<p><b>Presents a unified approach to parametric estimation, confidence intervals, hypothesis testing, and statistical modeling, which are uniquely based on the likelihood function</b></p> <p>This book addresses mathematical statistics for upper-undergraduates and first year graduate students, tying chapters on estimation, confidence intervals, hypothesis testing, and statistical models together to present a unifying focus on the likelihood function. It also emphasizes the important ideas in statistical modeling, such as sufficiency, exponential family distributions, and large sample properties. <i>Mathematical Statistics: An Introduction to Likelihood Based Inference</i> makes advanced topics accessible and understandable and covers many topics in more depth than typical mathematical statistics textbooks. It includes numerous examples, case studies, a large number of exercises ranging from drill and skill to extremely difficult problems, and many of the important theorems of mathematical statistics along with their proofs.</p> <p>In addition to the connected chapters mentioned above, <i>Mathematical Statistics</i> covers likelihood-based estimation, with emphasis on multidimensional parameter spaces and range dependent support. It also includes a chapter on confidence intervals, which contains examples of exact confidence intervals along with the standard large sample confidence intervals based on the MLE’s and bootstrap confidence intervals. There’s also a chapter on parametric statistical models featuring sections on non-iid observations, linear regression, logistic regression, Poisson regression, and linear models. </p> <ul> <li>Prepares students with the tools needed to be successful in their future work in statistics data science</li> <li>Includes practical case studies including real-life data collected from Yellowstone National Park, the Donner party, and the Titanic voyage</li> <li>Emphasizes the important ideas to statistical modeling, such as sufficiency, exponential family distributions, and large sample properties</li> <li>Includes sections on Bayesian estimation and credible intervals</li> <li>Features examples, problems, and solutions</li> </ul> <p><i>Mathematical Statistics: An Introduction to Likelihood Based</i> <i>Inference</i> is an ideal textbook for upper-undergraduate and graduate courses in probability, mathematical statistics, and/or statistical inference.</p>