What is bootstrap in statistics?

What is bootstrap in statistics?

• A. A resampling technique using sampling with replacement from observed data to estimate the sampling distribution.
• B. A parametric method assuming normality.
• C. A time series decomposition method.
• D. A hypothesis test.

Answer: (A)

Bootstrap is a resampling approach that uses sampling with replacement from the observed data to approximate the sampling distribution of a statistic. The idea is simple: take many bootstrap samples, each the same size as the original data, by drawing observations with replacement. For each resample, compute the statistic you care about (like the mean, median, regression coefficient, etc.). The spread of those computed values across all bootstrap samples forms an empirical distribution that serves as an estimate of the true sampling distribution of that statistic. This method is powerful because it makes few assumptions about the underlying population (it's largely nonparametric) and it can be used to estimate standard errors, construct confidence intervals, and assess bias for a wide range of statistics, even when theoretical formulas are complicated or unknown. It also helps when the data don’t meet the normality assumptions required by many classical methods. It’s not describing a parametric method that assumes a normal distribution, nor a time series decomposition technique, nor a hypothesis test—the bootstrap itself is about approximating how a statistic behaves across repeated samples from the data.

Bootstrap is a resampling approach that uses sampling with replacement from the observed data to approximate the sampling distribution of a statistic. The idea is simple: take many bootstrap samples, each the same size as the original data, by drawing observations with replacement. For each resample, compute the statistic you care about (like the mean, median, regression coefficient, etc.). The spread of those computed values across all bootstrap samples forms an empirical distribution that serves as an estimate of the true sampling distribution of that statistic.

This method is powerful because it makes few assumptions about the underlying population (it's largely nonparametric) and it can be used to estimate standard errors, construct confidence intervals, and assess bias for a wide range of statistics, even when theoretical formulas are complicated or unknown. It also helps when the data don’t meet the normality assumptions required by many classical methods.

It’s not describing a parametric method that assumes a normal distribution, nor a time series decomposition technique, nor a hypothesis test—the bootstrap itself is about approximating how a statistic behaves across repeated samples from the data.