Elements of Modern Asymptotic Theory with Statistical Applications |
Contents
Probability and measure | 1 |
Concepts of asymptotic convergence | 48 |
Further asymptotic theory with applications in regression | 82 |
Likelihood and associated concepts | 106 |
Maximum likelihood and asymptotic theory | 129 |
Metric spaces and stochastic processes | 155 |
Brownian motion and weak convergence | 171 |
Applications of weak convergence | 193 |
Dependent random variables and mixing | 215 |
Dependent sequences and martingales | 238 |
| 255 | |
Common terms and phrases
almost-sure convergence applies argument assumed assumption asymptotic distribution asymptotic normality asymptotic theory Borel Brownian bridge Brownian motion Chapter consider consistent constructed context continuous convergence in probability converges in distribution converges to zero covariance defined definition discussion distribution function Donsker's Theorem evaluated Example finite number follows function F given identically distributed implies independent inequality interval Lebesgue measure limiting distribution Lindeberg condition mapping Markov's inequality martingale matrix mixing moments multivariate normal distribution normal random variable notation null hypothesis o-field parameter partial-sum process probability measure probability space properties random walk real line result S₁ sample space score equation Section sequence of random sigma-field Sn(t standardised stationary statistic Stieltjes integral stochastic process subsets term tion vector random variable weak convergence WLLN X₁ y₁ zero mean σ²