Estimating with Bootstrapping
A computer-intensive resampling method for estimating parameters when traditional conditions are not met.
What is Bootstrapping?
Bootstrapping is a computer-intensive resampling method used to estimate parameters when:
- The underlying distribution is unknown
- Conditions for parametric statistics are not met
- You want a distribution-free approach
Key Idea: Treat the sample data as the population and repeatedly resample with replacement.
The Bootstrap Process
Treat Sample as Population
Consider your original sample data as representing the population.
Resample with Replacement
Draw B resamples (e.g., 1000 or 2000) of the same size n, with replacement.
Calculate Statistic
For each resample, calculate the desired statistic (mean, median, proportion, etc.).
Build Distribution
Create a distribution of the B statistics you've calculated.
Interactive Bootstrap Simulation
Watch resampling with replacement build a sampling distribution
Original Sample (n = 10)
How it works: Each bootstrap sample is drawn with replacement from the original data. Notice how some values appear multiple times and others may be missing in each resample. The distribution of all these sample means approximates the sampling distribution, allowing us to construct confidence intervals without assuming a specific population distribution.
Percentile Method
Use the percentile method to find the confidence interval from the bootstrap distribution.
For a 95% Confidence Interval:
90% CI: 5th and 95th percentiles
99% CI: 0.5th and 99.5th percentiles
When to Use Bootstrapping
Use When
- • Population distribution is unknown
- • Sample size is small
- • Parametric assumptions not met
- • Estimating complex statistics
Advantages
- • No distribution assumptions
- • Works for any statistic
- • Easy to implement with software
- • Provides visual interpretation
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