Presents a unified approach to parametric estimation, hypothesis testing, confidence intervals, and statistical modeling, which are uniquely based on the likelihood function. This ebook, Mathematical Statistics: An Introduction to Likelihood Based Inference (PDF), addresses mathematical statistics for first year graduate and upper-undergraduates students, tying chapters on estimation, hypothesis testing, confidence intervals, and statistical models together to present a unifying focus on the likelihood function. It also emphasizes the important ideas in statistical modeling, such as exponential family distributions, sufficiency, and large sample properties. Rossi’s Mathematical Statistics: An Introduction to Likelihood Based Inference PDF makes advanced topics accessible and understandable and covers many topics in more depth than typical mathematical statistics textbooks. It includes numerous case studies, great examples, 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.
In addition to the connected chapters mentioned above, Mathematical Statistics 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 Poisson regression, non-iid observations, logistic regression, linear regression, and linear models.
- Features good examples, problems, and solutions
- Includes sections on Bayesian estimation and credible intervals
- Prepares college students with the tools needed to be successful in their future work in statistics data science
- Emphasizes the important ideas to statistical modeling, such as exponential family distribution, sufficiency, and large sample properties
- Includes practical case studies including real-life data collected from the Donner party, Yellowstone National Park, and the Titanic voyage
Mathematical Statistics: An Introduction to Likelihood Based Inference is an ideal etextbook for graduate and upper-undergraduate courses in mathematical statistics, probability, and/or statistical inference.