Advanced Statistical Inference
This course aims at describing the advanced level topics in statistical methods and statistical inference. This course would prepare students to have a strong base in basic statistics that would help them in undertake basic and applied research in Statistics.
- Robust estimation and robust tests. Asymptotic techniques, Bayesian inference. Estimation of density function, Conditional inference, Detection and handling of outliers in statistical data.
- Loglinear models, saturated models, hierarchical models, Analysis of multi - dimensional contingency tables.
- Density Estimation: Density Estimation in the Exploration and Presentation of Data. Survey of existing methods. The Kernel method for Univariate Data: Rosenblatts naïve estimator, its bias and variance. Consistency of general Kernel estimators, MSE and IMSE. Asymptotic normality of Kernel estimates of density. Estimation of distribution by method of kernels.
- Consistency and asymptotic normality (CAN) of real and vector parameters. Invariance of consistency under continuous transformation. Invariance of CAN estimators under differentiable transformations, generation of CAN estimators using central limit theorem. Exponential class of densities and multinomial distribution, Cramer-Huzurbazar theorem, method of scoring.
Robust estimation and robust tests, Detection and Handling of Outliers in Statistical Data, Conditional Inference, Bayesian Inference, Log-linear Models, Saturated Models and Hierarchal Models, Estimation of Density Function, Analysis of Multi-dimensional Contingency Tables.