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Compression-Based Methods of Statistical Analysis and Prediction of Time Series 1st ed. 2016 [Kõva köide]

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  • Formaat: Hardback, 144 pages, kõrgus x laius: 235x155 mm, kaal: 3613 g, 21 Illustrations, color; 8 Illustrations, black and white; IX, 144 p. 29 illus., 21 illus. in color., 1 Hardback
  • Ilmumisaeg: 27-May-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319322516
  • ISBN-13: 9783319322513
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Compression-Based Methods of Statistical Analysis and Prediction of Time Series 1st ed. 2016Suurem pilt
  • Formaat: Hardback, 144 pages, kõrgus x laius: 235x155 mm, kaal: 3613 g, 21 Illustrations, color; 8 Illustrations, black and white; IX, 144 p. 29 illus., 21 illus. in color., 1 Hardback
  • Ilmumisaeg: 27-May-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319322516
  • ISBN-13: 9783319322513
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319322513.html
Märksõnad:
Universal codes efficiently compress sequences generated by stationary and ergodic sources with unknown statistics, and they were originally designed for lossless data compression. In the meantime, it was realized that they can be used for solving important problems of prediction and statistical analysis of time series, and this book describes recent results in this area.The first chapter introduces and describes the application of universal codes to prediction and the statistical analysis of time series; the second chapter describes applications of selected statistical methods to cryptography, including attacks on block ciphers; and the third chapter describes a homogeneity test used to determine authorship of literary texts.The book will be useful for researchers and advanced students in information theory, mathematical statistics, time-series analysis, and cryptography. It is assumed that the reader has some grounding in statistics and in information theory.

Statistical Methods Basedon Universal Codes.- Applications to Cryptography.- SCOT-Modeling andNonparametric Testing of Stationary Strings.

Arvustused

The book under review describes several recent results on Universal Codes. its reading may be useful for non-mathematical professionals interested in handling large data sources. (Oscar Bustos, zbMATH 1360.94001, 2017)

1 Statistical Methods Based on Universal Codes
1(44)
1.1 Introduction
1(1)
1.2 Definitions and Statements of the Problems
2(12)
1.2.1 Estimation and Prediction for I.I.D. Sources
2(6)
1.2.2 Consistent Estimations and On-Line Predictors for Markov and Stationary Ergodic Processes
8(3)
1.2.3 Hypothesis Testing
11(1)
1.2.4 Codes
12(2)
1.3 Finite Alphabet Processes
14(6)
1.3.1 The Estimation of (Limiting) Probabilities
14(1)
1.3.2 Prediction
15(1)
1.3.3 Problems with Side Information
16(1)
1.3.4 The Case of Several Independent Samples
17(3)
1.4 Hypothesis Testing
20(1)
1.4.1 Goodness-of-Fit or Identity Testing
20(1)
1.4.2 Testing for Serial Independence
20(1)
1.5 Examples of Hypothesis Testing
21(1)
1.6 Real-Valued Time Series
22(6)
1.6.1 Density Estimation and Its Application
22(3)
1.6.2 Example of Forecasting
25(3)
1.7 The Hypothesis Testing for Infinite Alphabet
28(1)
1.8 Conclusion
29(16)
Appendix
29(13)
References
42(3)
2 Applications to Cryptography
45(26)
2.1 Introduction
45(2)
2.2 Data Compression Methods as a Basis for Randomness Testing
47(3)
2.2.1 Randomness Testing Based on Data Compression
47(3)
2.2.2 Randomness Testing Based on Universal Codes
50(1)
2.3 Two New Tests for Randomness and Two-Faced Processes
50(5)
2.3.1 The "Book Stack" Test
51(1)
2.3.2 The Order Test
52(1)
2.3.3 Two-Faced Processes and the Choice of the Block Length for a Process Testing
53(2)
2.4 The Experiments
55(3)
2.5 Analysis of Stream Ciphers and Random Number Generators Used in Cryptography
58(2)
2.5.1 The Distinguishing Attack on ZK-Crypt Cipher
59(1)
2.5.2 Analysis of the PRNG RC4
59(1)
2.6 A Statistical Attack on Block Ciphers
60(11)
2.6.1 Cryptanalysis of Block Ciphers
60(2)
2.6.2 Description of the Attack
62(2)
2.6.3 Variants and Optimizations
64(1)
2.6.4 Experiments with RC5
65(2)
Appendix
67(1)
References
68(3)
3 SCOT-Modeling and Nonparametric Testing of Stationary Strings
71
3.1 Introduction
71(2)
3.2 Theory of UC-Based Discrimination
73(6)
3.2.1 Homogeneity Testing with UC
73(2)
3.2.2 Preliminaries
75(1)
3.2.3 Main Results
76(1)
3.2.4 Sketch of AN Justification Under the Null-Hypothesis
77(1)
3.2.5 Preceding Work
78(1)
3.3 SCOT-Modeling
79(10)
3.3.1 m-MC Reduction to MC on Am
80(1)
3.3.2 Counterexample
81(1)
3.3.3 1-MC Model Induced by SCOT
81(1)
3.3.4 Stationary Distribution for Model
82(1)
3.3.5 `Comb' Model Dm
83(1)
3.3.6 Models 2
84(5)
3.4 Limit Theorems for Additive Functions of SCOT Trajectories
89(7)
3.4.1 SCOT Models Admitting Continuous Time Limit
90(1)
3.4.2 Continuous Time Limit
90(1)
3.4.3 `Thorny' THa,b SCOT Model
91(1)
3.4.4 Asymptotic Normality for Additive Functions of m-MC Trajectories
92(1)
3.4.5 Asymptotic Expansion for Additive Functions
92(1)
3.4.6 Nonparametric Homogeneity Test
93(1)
3.4.7 Exponential Tails for Log-Likelihood Functions
93(1)
3.4.8 Application to the STI Analysis Under Colored Noise
94(2)
3.5 SCOT Homogeneity Test for Real Data
96(13)
3.5.1 NASDAQ Data
97(1)
3.5.2 Results for Three PC
98(1)
3.5.3 Results for Two PC
98(1)
3.5.4 Results for One PC
99(1)
3.5.5 Prediction Accuracy
99(1)
3.5.6 Follow-Up Analysis
100(1)
3.5.7 Comparison with GARCH
101(1)
3.5.8 GARCH and Epicycles
102(1)
3.5.9 Madison vs. Hamilton Discrimination of Styles
103(4)
3.5.10 Helium Emissions and Seismic Events
107(2)
3.5.11 Discussion and Conclusions
109(1)
3.6 UC-Based Authorship Attribution
109
3.6.1 CCC-and CC-Statistics
111(2)
3.6.2 CCC-Sample- Size Requirements
113(1)
3.6.3 Naive Explanation of CCC-Consistency on Toy Example
113(1)
3.6.4 Methodology
114(2)
3.6.5 Follow-Up Analysis of the Most Contributing Patterns
116(1)
3.6.6 Results
117(2)
3.6.7 Brief Survey of Micro-Stylometry Tools
119(3)
3.6.8 Attribution of Literary Texts
122(1)
3.6.9 Two Translations of Shakespeare Sonnets
122(1)
3.6.10 Two Books of Isaiah
123(2)
3.6.11 Two Novels of the Same Author
125(1)
3.6.12 Inhomogeneity of an Early Sholokhov's Novel
125(5)
3.6.13 Attribution of Federalist Papers
130(3)
3.6.14 The Shakespeare Controversy
133(3)
3.6.15 Amores et al. Versus Rape of Lucrece
136(2)
3.6.16 Hero and Leander Versus Its Continuation
138(2)
3.6.17 Comparison with Poems Chapman i, i = 1,2,3
140(7)
References
147