Can bootstrap help reduce variance
Company: Google
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Onsite
An interviewer asks: “Can bootstrap help reduce variance?”
Answer this question precisely. Distinguish between:
1) Using the bootstrap to **estimate** variance/standard error.
2) Using bootstrap-related ideas to **actually reduce** the variance of an estimator.
Give at least one concrete example where bootstrap **does not** reduce variance, and one example where bootstrap-style resampling **can** reduce variance (or yields a lower-variance predictor), and explain why.
Quick Answer: This question evaluates understanding of bootstrap resampling, the distinction between estimating an estimator’s variance and methods that actually reduce estimator variance, and related ensemble reasoning for a Data Scientist role in the Statistics & Math domain.