| Area | Key Idea | Representative Method | |------|----------|------------------------| | | (p) comparable or larger than (n) | Lasso, Ridge, Elastic Net | | Non‑parametric inference | Infinite‑dimensional parameter spaces | Kernel density estimation, empirical processes | | Robust statistics | Resistance to outliers/model misspecification | M‑estimators, Huber loss | | Sequential analysis | Data accrue over time; early stopping | SPRT, Bayesian monitoring | | Causal inference | Distinguish correlation from causation | Potential outcomes, instrumental variables | | Machine learning theory | Statistical guarantees for algorithms | VC dimension, Rademacher complexity, PAC bounds |
| Model | Parameter(s) | Typical Setting | |-------|--------------|-----------------| | | (p\in(0,1)) | Binary outcomes | | Binomial | ((n,p)) | Number of successes in (n) trials | | Normal | ((\mu,\sigma^2)) | Continuous measurements | | Exponential family | (\theta) (canonical) | Wide range; includes Poisson, Gamma, etc. | | Non‑parametric | None (or infinite‑dimensional) | Distribution-free methods | | Area | Key Idea | Representative Method
"Mathematical Statistics" by Pramod Kumar Vitthal is a comprehensive textbook that covers the fundamental principles of mathematical statistics. The book provides a rigorous treatment of statistical theory, including probability, random variables, statistical inference, and hypothesis testing. Written in a clear and concise manner, the textbook is designed to cater to the needs of students and researchers in various fields, including engineering, economics, and social sciences. Written in a clear and concise manner, the
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