Course Information & Syllabus
Syllabus
Paper – I : Research Methodology
- Unit I: Paradigms of Research: Creative Reading, Critical Reading, Critical Thinking and Literature Review. Steps in finding a Research problem. Research Strategies: Experiments, Design and Creation, surveys, case study research, Action research, bind Ethnography. Data gathering methods. Information Technology in Research Use of word processor, spreadsheets, presentation managers; Internet concepts, searching the web, Managing personal blogs, Open source software and its use in Research (emphasis on R).
- Unit II: Monte Carlo techniques : Simulation from univariate and multivariate distribution, Importance sampling, Numerical methods for integration, differentiation. Programming in R for implementing these techniques Macros in MINITAB & MATLAB.
- Unit III : Convergence of real numbers. Limit inferior and limit superior of the sequences. Various modes of convergence of sequence of random variables.
- Unit IV: Multivariate Data analysis principal components, factor analysis, cluster analysis. Implementation of these techniques using statistical software.
Paper – II : Recent Trends in Statistics
- Unit I : Introduction to Bootstrap and Jackknife methods, Applications in point estimation, and confidence intervals cross-validation of prediction. Markov Chain Monte Carlo Methods and applications EM algorithm MetropolisHasting Algorithm, Gibbs Sampling.
- Unit II : Artificial Neural Network : fundamental concept and models of Artificial Neural systems, feed forward and feedback networks, perception learning rule. Single layer perception classifiers. Multilayer feed forward networks. Support vector Machines: Problem formulation, Lagrangian theory, Duality, support
vector classification, support vector regression implementation techniques.
- Unit III: Generalized Linear Models: The exponential family, Likelihood Theory and moments, Linear structure and the link functions, estimation procedures Newton Rap son, WLS, IWLS, Residuals and Model fit.
- Unit IV: Nonparametric Regression: Basic idea of smoothing, spline smoothing, kernel regression. Nonparametric designing estimation. The naïve estimator, The Kernel estimator, The nearest neighbour method, The variable Kernel Method, Orthogonal series estimators, Maximum penalized likelihood estimators, General weight function estimators.
Paper – III : Statistical Analysis of Circular Data (Optional Paper)
Paper – III : Topic in Asymptotic Inference (Optional Paper)
Paper – III : Topic in Distribution Theory (Optional Paper)
Paper – III : Applied Regression Analysis (Optional Paper)
Paper – III : Topic in Discrete Multivariate Analysis (Optional Paper)
Paper – III : Advanced Topics in Sampling Theory (Optional Paper)
Paper – III : Advanced Design of Experiments (Optional Paper)
Paper – III : Topic in Reliability Analysis (Optional Paper)
Paper – III : Statistical Quality Control (Optional Paper)
Paper – III : Advanced Inference (Optional Paper)
Paper – III : Reliability Theory and Survival Analysis (Optional Paper)
