|
|
|
|
| LEADER |
03934nam a22005055i 4500 |
| 001 |
6460 |
| 003 |
DE-He213 |
| 005 |
20130725190723.0 |
| 007 |
cr nn 008mamaa |
| 008 |
100301s2009 gw | s |||| 0|eng d |
| 020 |
# |
# |
|a 9783540856368
|9 978-3-540-85636-8
|
| 024 |
7 |
# |
|a 10.1007/978-3-540-85636-8
|2 doi
|
| 050 |
# |
4 |
|a QA273.A1-274.9
|
| 050 |
# |
4 |
|a QA274-274.9
|
| 072 |
# |
7 |
|a PBT
|2 bicssc
|
| 072 |
# |
7 |
|a PBWL
|2 bicssc
|
| 072 |
# |
7 |
|a MAT029000
|2 bisacsh
|
| 082 |
0 |
4 |
|a 519.2
|2 23
|
| 100 |
1 |
# |
|a Peą, Victor H.
|e author.
|
| 245 |
1 |
0 |
|a Self-Normalized Processes
|b Limit Theory and Statistical Applications /
|c by Victor H. Peą, Tze Leung Lai, Qi-Man Shao.
|h [electronic resource] :
|
| 264 |
# |
1 |
|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg,
|c 2009.
|
| 300 |
# |
# |
|a XIII, 275 p.
|b online resource.
|
| 336 |
# |
# |
|a text
|b txt
|2 rdacontent
|
| 337 |
# |
# |
|a computer
|b c
|2 rdamedia
|
| 338 |
# |
# |
|a online resource
|b cr
|2 rdacarrier
|
| 347 |
# |
# |
|a text file
|b PDF
|2 rda
|
| 490 |
1 |
# |
|a Probability and its Applications,
|x 1431-7028
|
| 505 |
0 |
# |
|a 1. Introduction -- Part I Independent Random Variables -- 2. Classical Limit Theorems and Preliminary Tools -- 3. Self-Normalized Large Deviations -- 4. Weak Convergence of Self-Normalized Sums -- 5. Stein<U+0019>s Method and Self-Normalized Berry<U+0013>Esseen Inequality -- 6. Self-Normalized Moderate Deviations and Law of the Iterated Logarithm -- 7. Cramř-type Moderate Deviations for Self-Normalized Sums -- 8. Self-Normalized Empirical Processes and U-Statistics -- Part II Martingales and Dependent Random Vectors -- 9. Martingale Inequalities and Related Tools -- 10. A General Framework for Self-Normalization -- 11. Pseudo-Maximization via Method of Mixtures -- 12. Moment and Exponential Inequalities for Self-Normalized Processes -- 13. Laws of the Iterated Logarithm for Self-Normalized Processes and Martingales -- 14. Multivariate Matrix-Normalized Processes -- Part III Statistical Applications -- 15. The t-Statistic and Studentized Statistics -- 16. Self-Normalization and Approximate Pivots for Bootstrapping -- 17. Self-Normalized Martingales and Pseudo-Maximization in Likelihood or Bayesian Inference -- 18. Information Bounds and Boundary Crossing Probabilities for Self-Normalized Statistics in Sequential Analysis -- References -- Index.
|
| 520 |
# |
# |
|a Self-normalized processes are of common occurrence in probabilistic and statistical studies. A prototypical example is Student's t-statistic introduced in 1908 by Gosset, whose portrait is on the front cover. Due to the highly non-linear nature of these processes, the theory experienced a long period of slow development. In recent years there have been a number of important advances in the theory and applications of self-normalized processes. Some of these developments are closely linked to the study of central limit theorems, which imply that self-normalized processes are approximate pivots for statistical inference. The present volume covers recent developments in the area, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales. This is the first book that systematically treats the theory and applications of self-normalization.
|
| 650 |
# |
0 |
|a Mathematics.
|
| 650 |
# |
0 |
|a Distribution (Probability theory).
|
| 650 |
# |
0 |
|a Mathematical statistics.
|
| 650 |
1 |
4 |
|a Mathematics.
|
| 650 |
2 |
4 |
|a Probability Theory and Stochastic Processes.
|
| 650 |
2 |
4 |
|a Statistical Theory and Methods.
|
| 700 |
1 |
# |
|a Lai, Tze Leung.
|e author.
|
| 700 |
1 |
# |
|a Shao, Qi-Man.
|e author.
|
| 710 |
2 |
# |
|a SpringerLink (Online service)
|
| 773 |
0 |
# |
|t Springer eBooks
|
| 776 |
0 |
8 |
|i Printed edition:
|z 9783540856351
|
| 830 |
# |
0 |
|a Probability and its Applications,
|x 1431-7028
|
| 856 |
4 |
0 |
|u https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-85636-8
|
| 912 |
# |
# |
|a ZDB-2-SMA
|
| 950 |
# |
# |
|a Mathematics and Statistics (Springer-11649)
|