2 Parameter Estimation
In this section, we study one of the central topics in statistics: parameter estimation. This is the beginning of our tour! The section is organized as follows:
- 1.
- Fundamentals
- 2.
- Methods of Estimation
- 3.
- Large Sample Theory
This section mainly follows STAT 210A at UC Berkeley [21], STAT 300A and STAT 300B at Stanford University [13, 6], and Mathematical Statistics at Peking University, taught by Fang Yao [27]. I also referred to the book Theoretical Statistics [5].
2.1 Fundamentals
2.2 Methods of Estimation
2.2.1 Unbiased Estimation
2.2.2 Bayes Estimators
2.2.3 Minimax Estimators
2.2.4 James Stein Estimator
2.2.5 How to Derive an Estimator
2.3 Large Sample Theory
2.3.1 Delta Method
2.3.2 Fisher Information
2.2 Methods of Estimation
2.2.1 Unbiased Estimation
2.2.2 Bayes Estimators
2.2.3 Minimax Estimators
2.2.4 James Stein Estimator
2.2.5 How to Derive an Estimator
2.3 Large Sample Theory
2.3.1 Delta Method
2.3.2 Fisher Information