
Large Sample Techniques for Statistics
Jiming Jiang(Author)
Springer (Publisher)
2nd Edition
Published on 6. April 2023
Book
Paperback/Softback
XV, 685 pages
978-3-030-91697-8 (ISBN)
Description
In a way, the world is made up of approximations, and surely there is no exception in the world of statistics. In fact, approximations, especially large sample approximations, are very important parts of both theoretical and - plied statistics.TheGaussiandistribution,alsoknownasthe normaldistri- tion,is merelyonesuchexample,dueto thewell-knowncentrallimittheorem. Large-sample techniques provide solutions to many practical problems; they simplify our solutions to di?cult, sometimes intractable problems; they j- tify our solutions; and they guide us to directions of improvements. On the other hand, just because large-sample approximations are used everywhere, and every day, it does not guarantee that they are used properly, and, when the techniques are misused, there may be serious consequences. 2 Example 1 (Asymptotic? distribution). Likelihood ratio test (LRT) is one of the fundamental techniques in statistics. It is well known that, in the 2 "standard" situation, the asymptotic null distribution of the LRT is?,with the degreesoffreedomequaltothe di?erencebetweenthedimensions,de?ned as the numbers of free parameters, of the two nested models being compared (e.g., Rice 1995, pp. 310). This might lead to a wrong impression that the 2 asymptotic (null) distribution of the LRT is always? . A similar mistake 2 might take place when dealing with Pearson's? -test-the asymptotic distri- 2 2 bution of Pearson's? -test is not always? (e.g., Moore 1978).
More details
Product info
Paperback
Series
Edition
2nd ed. 2022
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Edition type
Revised edition
Illustrations
7
2 farbige Abbildungen, 7 s/w Abbildungen
XV, 685 p. 9 illus., 2 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 38 mm
Weight
1048 gr
ISBN-13
978-3-030-91697-8 (9783030916978)
DOI
10.1007/978-3-030-91695-4
Schweitzer Classification
Other editions
Additional editions

Jiming Jiang
Large Sample Techniques for Statistics
Book
04/2022
2nd Edition
Springer
€96.29
Shipment within 7-9 days
Person
Jiming Jiang
is Professor of Statistics and a former Director of Statistical Laboratory at the University of California, Davis. He is a prominent researcher in the fields of mixed effects models, small area estimation, model selection, and statistical genetics. He is the author of
Linear and Generalized Linear Mixed Models and Their Applications, 2nd Edition
(Springer 2021),
Robust Mixed Model Analysis
(2019),
Asymptotic Analysis of Mixed Effects Models: Theory, Applications, and Open Problems
(2017), and
The Fence Methods
(with T. Ngyuen, 2016). Jiming Jiang has been editorial board member of
The Annals of Statistics
and
Journal of the American Statistical Association
, among others. He is a Fellow of the American Association for the Advancement of Science, the American Statistical Association, and the Institute of Mathematical Statistics; an elected member of the International Statistical Institute; and a Yangtze River Scholar (Chaired Professor, 2017-2020).
Content
Chapter 1. The -d Arguments.- Chapter 2. Modes of Convergence.- Chapter 3. Big O, Small o, and the Unspecified c.- Chapter 4. Asymptotic Expansions.- Chapter 5. Inequalities.- Chapter 6. Sums of Independent Random Variables.- Chapter 7. Empirical Processes.- Chapter 8. Martingales.- Chapter 9. Time and Spatial Series.- Chapter 10. Stochastic Processes.- Chapter 11. Nonparametric Statistics.- Chapter 12. Mixed Effects Models.- Chapter 13. Small-Area Estimation.- Chapter 14. Jackknife and Bootstrap.- Chapter 15. Markov-Chain Monte Carlo.- Chapter 16. Random Matrix Theory.