Bootstrap Variance Estimation

Using bootstrapping, we can approximate by simulation. Here, means the variance of if the distribution of the data is .. This is done by simulating from and then compute . This constitutes one draw from the distribution of .

Observation

How do we simulate from ? Notice that puts mass at each data points . Therefore, drawing an observation from is equivalent to drawing one point at random from the original dataset. Thus, to simulate it suffices to draw observations with replacement from .

Bootstrap Variance Estimation

1. Draw .
2. Compute .
3. Repeat steps 1 and 2, times, to get .
4. Let

Sources

• Wasserman, L. (2010). All of Statistics: A concise Course in Statistical Inference. Chapter 8.2.