Table of Contents
PART 1. MATHEMATICAL STATISTICS
Chapter 1. Introduction to Mathematical Statistics
1.2. Examples of statistics problems
Chapter 2. Principles of Decision Theory
2.2. The problem of choosing a decision function11
2.3. Principles of Bayesian statistics
2.5. Criticism of decision theory – the asymptotic point of view
Chapter 3. Conditional Expectation
3.3. Conditional probabilities and conditional distributions
Chapter 4. Statistics and Sufficiency
4.1. Samples and empirical distributions
4.3. Examples of sufficient statistics – an exponential model
4.4. Use of a sufficient statistic
5.2. Sufficiency and completeness
5.3. The maximum-likelihood method
5.4. Optimal unbiased estimators
5.5. Efficiency of an estimator
5.6. The linear regression model
Chapter 6. Hypothesis Testing and Confidence Regions
6.2. The Neyman–Pearson (NP) lemma
6.3. Multiple hypothesis tests (general methods)
6.4. Case where the ratio of the likelihoods is monotonic
6.5. Tests relating to the normal distribution
6.6. Application to estimation: confidence regions
Chapter 7. Asymptotic Statistics
7.2. Consistency of the maximum likelihood estimator
7.3. The limiting distribution of the maximum likelihood estimator
7.4. The likelihood ratio test
Chapter 8. Non-Parametric Methods and Robustness
8.2. Non-parametric estimation
PART 2. STATISTICS FOR STOCHASTIC PROCESSES
Chapter 9. Introduction to Statistics for Stochastic Processes
9.1. Modeling a family of observations
9.3. Statistics for stochastic processes
Chapter 10. Weakly Stationary Discrete-Time Processes
10.1. Autocovariance and spectral density
10.2. Linear prediction and Wold decomposition
10.3. Linear processes and the ARMA model
10.4. Estimating the mean of a weakly stationary process
10.5. Estimating the autocovariance
10.6. Estimating the spectral density
Chapter 11. Poisson Processes – A Probabilistic and Statistical Study
11.2. The axioms of Poisson processes
11.4. Properties of the Poisson process
11.5. Notions on generalized Poisson processes
11.6. Statistics of Poisson processes
Chapter 12. Square-Integrable Continuous-Time Processes
12.4. Mean-square differentiation
12.5. The Karhunen–Loeve theorem
12.7. Notions on weakly stationary continuous-time processes
Chapter 13. Stochastic Integration and Diffusion Processes
13.3. Processes defined by stochastic differential equations and stochastic integrals
13.4. Notions on statistics for diffusion processes
14.1. Autoregressive processes
14.2. Moving average processes
14.5. Statistics of ARMA processes
14.6. Multidimensional processes
15.2. Empirical methods of prediction
15.3. Prediction in the ARIMA model
15.4. Prediction in continuous time
Chapter 16. Elements of Probability Theory
16.1. Measure spaces: probability spaces
16.2. Measurable functions: real random variables
16.3. Integrating real random variables
A1.2. Distribution function of the standard normal distribution
A1.3. Density of the standard normal distribution
A1.4. Percentiles (tp) of Student’s distribution
A1.5. Ninety-fifth percentiles of Fisher–Snedecor distributions
A1.6. Ninety-ninth percentiles of Fisher–Snedecor distributions
A1.7. Percentiles 
of the χ2 distribution with n degrees of freedom
A1.8. Individual probabilities of the Poisson distribution
A1.9. Cumulative probabilities of the Poisson distribution
A1.10. Binomial coefficients 
for n ≤ 30 and 0 ≤ k ≤ 7