The exhaustive list of topics in Large Sample Statistical Methods in which we provide Help with Homework Assignment and Help with Project is as follows:
- Convergence of random variables and central limit theorems. Cramer-Wold device. Scheffe's theorem. Polya's theorem. Slutsky's theorem.
- Asymptotic distribution of transformed statistics. Derivation of the variance stabilizing formula.Asymptotic distribution of functions of sample moments like sample correlation coefficient, coefficient of variation, measures of skewness and kurtosis.
- Asymptotic distribution of order statistics including extreme order statistics. Bahadur's result on asymptotic behaviour of sample quantiles.
- Large sample properties of maximum likelihood estimates and the method of scoring.
- Large sample properties of parameter estimates in linear, nonlinear and generalized linear models.
- Pearson's chi-square statistic. Chi-square and likelihood ratio test statistics for simple hypotheses related to contingency tables. Heuristic proof for composite hypothesis with contingency tables.
- Asymptotic behaviour of posterior distributions and Bayes estimates, preferably without proof but using heuristic justification based on Laplace approximation.
- Large sample nonparametric inference.
- Sufficiency, minimal sufficiency and completeness. Factorization theorem. Convex loss and Rao-Blackwell theorem. Unbiased estimates and Cramer-Rao inequality. Stein estimate and shrinkage for multivariate normal mean.
- Bayes estimates and tests. Bayesian credible region. Non-informative priors.