• Nonparametric Regression

Kernel and local polynomial smoothing, penalized splines, smoothing splines and reproducing kernel Hilbert spaces, additive and partially linear models, and neural networks for high-dimensional regression. 

• Statistical Methods for Analysis with Missing Data 

Missing data mechanisms (MCAR, MAR, and MNAR); likelihood-based inference under ignorability, the EM algorithm, and observed-data likelihood; multiple imputation via chained equations (MICE) and Rubin's variance estimator; inverse probability weighting (IPW) and augmented IPW estimators; doubly robust estimation; sensitivity analysis and pattern mixture models for nonignorable (MNAR) missingness. Semiparametric theory including M-estimation and estimating equations, the influence function and approximation by averages, generalized estimating equations (GEE), weighted GEE (WGEE) for missing longitudinal data, Hilbert space geometry and the tangent space, semiparametric efficiency bounds, and asymptotic theory for semiparametric estimators. Methods for misspecified likelihoods including generalized Wald, score, and likelihood ratio tests under misspecification, quadratic inference functions, and connections between robust variance estimation and the sandwich estimator. 

• Optimal Design 

Studied model-based design frameworks and optimality criteria, including variance-based criteria (G, c, MV), eigenvalue-based criteria (D, A, E), bias/alias criteria, H-optimality and weighted optimality criteria for sets of estimable functions, and Bayesian optimality. Coverage included designs with and without nuisance factors, approximate designs, universal optimality, and design search algorithms (row-exchange, coordinate-exchange, and SMW-accelerated variants). 

• Survival Analysis (Independently Studied using Collett's Modelling Survival Data in Medical Research, 3rd Ed.)

Nonparametric estimation (Kaplan-Meier, log-rank tests), parametric survival models (Weibull, exponential), Cox proportional hazards regression, recurrent events, competing risks, and time-dependent covariates. 

• Bayesian Inference and Analysis 

Foundations of Bayesian inference including prior specification (conjugate, objective, empirical Bayes, and penalized complexity priors), posterior summarization, and predictive distributions; Bayesian theory (De Finetti's Theorem, Bernstein-von Mises, posterior consistency); hierarchical and generalized linear mixed models, missing data, and censoring; model selection via cross-validation, Bayes factors, and posterior predictive checks; MCMC methods (Gibbs, Metropolis-Hastings, slice, and Hamiltonian), INLA, ABC, and scalable methods (variational Bayes, stochastic gradient MCMC); and Bayesian approaches to high-dimensional models, Dirichlet processes, BART, and neural networks.