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Random variables and distributions in statistics
Likelihood and associated concepts
Maximum likelihood and asymptotic theory
Metric spaces and stochastic processes
Brownian motion and weak convergence
applies approach argument assumed assumption asymptotic bounded Brownian motion called Chapter condition consider consistent constant constructed context continuous convergence convergence in probability course defined definition density dependent derivative difference discussion distribution function element equal established estimator evaluated Example exist expectation expression fact Figure finite follows further given gives Hence holds hypothesis implies important independent infinite integral interest interval introduced known limit mapping martingale matrix mean measure metric mixing moments natural necessary normal Note null o-field observed parameter possible probability problem properties quantity random variables reason respect result sample satisfy score seen sequence shown shows space squares standardised stationary statistic stochastic structure term Theorem theory tion true usual valid variance vector weak WLLN zero