Эта книга представляет собой единое изложение параметрической оценки, доверительных интервалов, тестирования гипотез и статистических моделей, основанных на функции правдоподобия. Книга предназначена для студентов старших курсов и первых курсов магистратуры, объединяя главы об оценке, доверительных интервалах, тестировании гипотез и статистические модели, чтобы представить единый подход к функции правдоподобия. В книге также подчеркиваются важные идеи в статистическом моделировании, такие как достаточность, распределения экспоненциальной семьи и свойства больших выборок. “Математическая статистика: введение в вероятностные выводы на основе функции правдоподобия” делает продвинутые темы доступными и понятными и охватывает многие темы более глубоко, чем типичные учебники по математической статистике. Он включает многочисленные примеры, тематические исследования, большое количество упражнений, от упражнений до очень сложных задач, и многие важные теоремы математической статистики вместе с их доказательствами. В дополнение к вышеупомянутым связанным главам, “Математическая статистика” охватывает вероятностно-базированную оценку с акцентом на многомерные параметрические пространства и зависящую от диапазона поддержку.
This book deals with mathematical statistics based on an approach that centers around the likelihood function, making it usable for undergraduates at one level and graduate students at another. The topics covered and presented in this approach include parametric estimation; confidence intervals; hypothesis testing; and statistical model building. Emphasis has been placed on important aspects of statistical model research, such as sufficient statistics, exponential families, and inference in large samples. Mathematical Statistics provides a more profound approach to complex topics, offering a much deeper treatment than other textbooks provide. It makes material that is advanced topic available and intelligible, explores many subjects in depth, and provides numerous examples, cases, exercises, and valuable theorems with complete proofs. Statistical analyses and estimates with regards to likelihoods draw attention from this text, especially regarding multi-parameter estimations and variable dependent supports. A chapter about confidence intervals including both exact and approximate large-sample approaches is provided, as well as a section on parameter statistical models with content for regression analysis (including non time-series regression, linear, logistic, and Poisson), and factor analysis. These chapters not only educate on the material being introduced, but also allow students to gain practical experience applying statistical principles through cases studying real life technologies (like from Yellowstone national park, Donner Party, and Titanic's travels). In addition, this book emphasizes significance in reference to statistical modelling, intending to provide valuable information behind the two abundant ways of statistical approach: Frequentist (based on hypothesis tests) and Bayesian (approaching the estimation with confidence intervals/densities). This text is an invaluable asset for undergraduate students entering the field of statistics or pursuing graduate degrees, providing the necessary tools and play framework to get off on a successful footing.
Presents a unified approach...
Электронная Книга «Mathematical Statistics» написана автором Richard Rossi J. в году.
Минимальный возраст читателя: 0
Язык: Английский
ISBN: 9781118770979
Описание книги от Richard Rossi J.
Presents a unified approach to parametric estimation, confidence intervals, hypothesis testing, and statistical modeling, which are uniquely based on the likelihood function 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. Mathematical Statistics: An Introduction to Likelihood Based Inference 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. 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 non-iid observations, linear regression, logistic regression, Poisson regression, and linear models. Prepares students with the tools needed to be successful in their future work in statistics data science Includes practical case studies including real-life data collected from Yellowstone National Park, the Donner party, and the Titanic voyage Emphasizes the important ideas to statistical modeling, such as sufficiency, exponential family distributions, and large sample properties Includes sections on Bayesian estimation and credible intervals Features examples, problems, and solutions Mathematical Statistics: An Introduction to Likelihood Based Inference is an ideal textbook for upper-undergraduate and graduate courses in probability, mathematical statistics, and/or statistical inference.
