Lecture notes in statistics Asymptotic Efficiency of Statistical Estimators Vol. 7 - Masafumi Akahira, Kei Takeuchi - książka wyd. 1981

Opis

Lecture Notes in Statistics: Asymptotic Efficiency of Statistical Estimators, Vol. 7 is a technical volume focused on the concept of asymptotic efficiency in statistical estimation. Part of the Lecture Notes in Statistics series, this book presents a detailed exploration of how statistical estimators behave as sample sizes grow large, a topic that is central to both theoretical and applied statistics.

The primary aim of the book is to provide a thorough understanding of the asymptotic properties of estimators, particularly how their performance improves (or does not) as the amount of data increases. Asymptotic efficiency is a key measure in statistics that evaluates how well an estimator approximates the true parameter of a population when the sample size tends to infinity. Estimators with higher asymptotic efficiency are preferred because they achieve lower variance as the sample size increases.

The volume includes a variety of methods and models used to assess and improve the asymptotic efficiency of different estimators. Topics covered include the Cramér-Rao lower bound, the concept of unbiasedness, maximum likelihood estimators, and the theory of efficient estimators in the context of large samples. It also addresses the trade-offs involved in choosing between different estimation techniques based on their asymptotic properties.

The book is mathematically rigorous, providing theoretical proofs, theorems, and discussions on the conditions under which certain estimators are asymptotically efficient. Examples are presented to illustrate the practical applications of these concepts in real-world statistical problems, making the content accessible to both advanced students and professionals working in the field of statistics.

This volume is particularly relevant for those involved in statistical theory, econometrics, biostatistics, and any field that requires estimation techniques based on large datasets. It is an essential resource for researchers and practitioners who need to understand the performance of their statistical models in the asymptotic sense, helping them to make informed choices about the methods they use in their work.