Vor Ort
Merkzettel Warenkorb
Produktbild: Mathematical Statistics and Stochastic Processes
- 13%

Mathematical Statistics and Stochastic Processes

13% sparen

146,99 € UVP 169,00 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

14.05.2012

Verlag

John Wiley & Sons

Seitenzahl

304

Maße (L/B/H)

23,4/15,2/2,3 cm

Gewicht

544 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-84821-361-6

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

14.05.2012

Verlag

John Wiley & Sons

Seitenzahl

304

Maße (L/B/H)

23,4/15,2/2,3 cm

Gewicht

544 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-84821-361-6

EU-Ansprechpartner

Kolibri 360 GmbH
Ettore-Bugatti-Straße 6-14
51149 Köln
DE
produktsicherheit@kolibri360.de

Herstelleradresse

Wiley & Sons
1 Oldlands Way
PO22 9NQ Bognor Regis
GB
trade@wiley.com

Noch keine Bewertungen vorhanden

Verfassen Sie die erste Bewertung zu diesem Artikel

Helfen Sie anderen Kundinnen und Kunden durch Ihre Meinung.

Kundinnen und Kunden meinen

Bewertungen (0)
Die Leseprobe wird geladen.
  • Produktbild: Mathematical Statistics and Stochastic Processes
  • Preface xiii

    PART 1. MATHEMATICAL STATISTICS 1

    Chapter 1. Introduction to Mathematical Statistics 3

    1.1. Generalities 3

    1.2. Examples of statistics problems 4

    Chapter 2. Principles of Decision Theory 9

    2.1. Generalities 9

    2.2. The problem of choosing a decision function 11

    2.3. Principles of Bayesian statistics 13

    2.4. Complete classes 17

    2.5. Criticism of decision theory - the asymptotic pointof view 18

    2.6. Exercises 18

    Chapter 3. Conditional Expectation 21

    3.1. Definition 21

    3.2. Properties and extension 22

    3.3. Conditional probabilities and conditional distributions24

    3.4. Exercises 26

    Chapter 4. Statistics and Sufficiency 29

    4.1. Samples and empirical distributions 29

    4.2. Sufficiency 31

    4.3. Examples of sufficient statistics - an exponentialmodel 33

    4.4. Use of a sufficient statistic 35

    4.5. Exercises 36

    Chapter 5. Point Estimation 39

    5.1. Generalities 39

    5.2. Sufficiency and completeness 42

    5.3. The maximum-likelihood method 45

    5.4. Optimal unbiased estimators 49

    5.5. Efficiency of an estimator 56

    5.6. The linear regression model 65

    5.7. Exercises 68

    Chapter 6. Hypothesis Testing and Confidence Regions73

    6.1. Generalities 73

    6.2. The Neyman-Pearson (NP) lemma 75

    6.3. Multiple hypothesis tests (general methods) 80

    6.4. Case where the ratio of the likelihoods is monotonic 84

    6.5. Tests relating to the normal distribution 86

    6.6. Application to estimation: confidence regions 86

    6.7. Exercises 90

    Chapter 7. Asymptotic Statistics 101

    7.1. Generalities 101

    7.2. Consistency of the maximum likelihood estimator 103

    7.3. The limiting distribution of the maximum likelihoodestimator 104

    7.4. The likelihood ratio test 106

    7.5. Exercises 108

    Chapter 8. Non-Parametric Methods and Robustness 113

    8.1. Generalities 113

    8.2. Non-parametric estimation 114

    8.3. Non-parametric tests 117

    8.4. Robustness 121

    8.5. Exercises 124

    PART 2. STATISTICS FOR STOCHASTIC PROCESSES 131

    Chapter 9. Introduction to Statistics for StochasticProcesses 133

    9.1. Modeling a family of observations 133

    9.2. Processes 134

    9.3. Statistics for stochastic processes 137

    9.4. Exercises 138

    Chapter 10. Weakly Stationary Discrete-Time Processes141

    10.1. Autocovariance and spectral density 141

    10.2. Linear prediction and Wold decomposition 144

    10.3. Linear processes and the ARMA model 146

    10.4. Estimating the mean of a weakly stationary process 149

    10.5. Estimating the autocovariance 151

    10.6. Estimating the spectral density 151

    10.7. Exercises 155

    Chapter 11. Poisson Processes - A Probabilistic andStatistical Study 163

    11.1. Introduction 163

    11.2. The axioms of Poisson processes 164

    11.3. Interarrival time 166

    11.4. Properties of the Poisson process 168

    11.5. Notions on generalized Poisson processes 170

    11.6. Statistics of Poisson processes 172

    11.7. Exercises 177

    Chapter 12. Square-Integrable Continuous-Time Processes183

    12.1. Definitions 183

    12.2. Mean-square continuity 183

    12.3. Mean-square integration 184

    12.4. Mean-square differentiation 187

    12.5. The Karhunen-Loeve theorem 188

    12.6. Wiener processes 189

    12.7. Notions on weakly stationary continuous-time processes195

    12.8. Exercises 197

    Chapter 13. Stochastic Integration and Diffusion Processes203

    13.1. Itô integral 203

    13.2. Diffusion processes 206

    13.3. Processes defined by stochastic differential equations andstochastic integrals 212

    13.4. Notions on statistics for diffusion processes 215

    13.5. Exercises 216

    Chapter 14. ARMA Processes 219

    14.1. Autoregressive processes 219

    14.2. Moving average processes 223

    14.3. General ARMA processes 224

    14.4. Non-stationary models 226

    14.5. Statistics of ARMA processes 228

    14.6. Multidimensional processes 232

    14.7. Exercises 233

    Chapter 15. Prediction 239

    15.1. Generalities 239

    15.2. Empir