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1 poissons wlln postulates complete heterogeneity for the bernoulli random variables involved but implicitly assumes
1 explain the conclusion of bernsteins wlln and discuss which assumptions are crucial for the validity of the
1 compare and contrast convergence almost surely and rth-order convergence2 for modeling purposes specific distribution
1 explain how the clt can be extended beyond the scaled summations2 explain how the fclt improves upon the classical
1 explain the probabilistic structure of a wiener process2 explain how a brownian motion process can be changed into a
1 explain the probabilistic structure of a gaussian markov process2 explain how a gaussian markov stationary process
1 a markov chain is a special markov process explain2 explain the notion of a poisson process3 explain the
1 explain the relationship between the bernoulli and binomial distributions2 linear functions of normally distributed
1 explain the concept of the distribution of the sample2 explain why estimation testing and prediction amounts to
1 explain briefly the difference between descriptive statistics and statistical inference when faced with the problem
1 robustness is part of parametric statistical inference and is often believed part of non-parametric inference
1 compare and contrast parametric and non-parametric statistical inference2 non-parametric statistical models give rise
1 how does de finettis representation theorem provides a bridge between chance regularity and the notion of a simple
1 discuss von mises attempt to build a bridge between chance regularity and the notion of probability2 discuss de
1 explain briefly what a consistent estimator is what is the easiest way to prove consistency for estimators with
1 asymptotic normality of an estimator is an extension of the central limit theorem for functions of the sample beyond
1 explain the notion of the ideal estimator and explain intuitively how its definition relates to the properties of
1 comparing maximum likelihood and parametric method of moments estimators on efficiency grounds is not a very
consider the simple normal statistical modela derive the mles of microsigma2 and their sampling distributionsb derive
consider the simple laplace statistical model based on the probability modelderive the mle of u and compare it with the
consider the simple pareto statistical model based on the probability modelderive the mle of u and compare it with the
1 state the optimal properties of maximum likelihood estimators finite sample and asymptotic2 explain the difference
1 derive the iterative scheme for the score method in evaluating the mle first-order conditions in the case of the
1 discuss the notion of statistical adequacy and explain the role of misspecification testing in establishing it2
1 what do we mean by a uniformly most powerful test ump tests are scarceexplain2 explain the notions ofa unbiased test