COURSE OBJECTIVES:
To train students for planning statistical experiments or observations, analysis of data and statistical inference about population based on sample by use of standard statistical models and methods for:
1. Comparison and testing laws of distribution,
2. Regression analysis,
3. Model selection,
4. Interval and point estimation of model parameters and hypothesis testing,
5. Valuation of model fit,
6. Dimension reduction,
7. Classification/discrimination of data,
8. Analysis of survival based on censored data.
COURSE CONTENT:
1. Nonparametric methods for law comparison. Rank tests (Mann-Whitney-Wilcoxon statistics, Spearman's coefficient of correlation), Kolmogorov-Smirnov tests, Tests of normality (Lilliefors test), ROC curve.
2. Multivariate data. Normal distribution, Multiple confidence intervals and multiple testing, Multiple correlation, Partial correlation, Linear regression models (Kronecker product, Gauss-Markov properties, model selection), MANOVA and MANCOVA models, Allocation and discrimination, Principal component analysis (the best linear prediction).
3. Log-linear models. Parameter estimation, Prediction, Wald test, Model selection.
4. Computer intensive methods. Monte Carlo methods, Bootstraping, Cross-validation, Permutation tests.
5. Survival analysis. Kaplan-Meier estimator, Cox proportional-hazards model.
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