Jackknife
- Estimates a statistic’s bias and variance by systematically omitting observations and recalculating the statistic.
- Simple to implement and broadly applicable, but can be computationally intensive for large datasets.
- Assumes observations are independent, which may not hold in all real-world data.
Definition
Section titled “Definition”Jackknife is a statistical method used to estimate the bias and variance of a population statistic. It involves repeatedly leaving out one or more observations from a dataset and calculating the statistic of interest on each subset. The estimates from each subset are then compared to determine the overall bias and variance of the statistic.
Explanation
Section titled “Explanation”The jackknife procedure generates multiple estimates of the same statistic by forming subsets of the original dataset, each subset formed by omitting one or more observations. By comparing the statistic computed on each subset, practitioners obtain estimates of the estimator’s bias and its variance. The method is straightforward to apply to many population statistics and provides a way to assess the reliability of an estimator using only the observed data.
Examples
Section titled “Examples”Estimating a population mean
Section titled “Estimating a population mean”Suppose we have a dataset of 10 observations and want to estimate the population mean. Using the jackknife, leave out one observation at a time and calculate the mean of the remaining 9 observations. Repeat this for each observation to obtain 10 different estimates of the population mean, then compare these estimates to determine the overall bias and variance of the mean estimator.
Estimating a population standard deviation
Section titled “Estimating a population standard deviation”Suppose we have a dataset of 20 observations and want to estimate the population standard deviation. Using the jackknife, leave out one observation at a time and calculate the standard deviation of the remaining 19 observations. Repeat this for each observation to obtain 20 different estimates of the population standard deviation, then compare these estimates to determine the overall bias and variance of the standard deviation estimator.
Use cases
Section titled “Use cases”- Estimating bias and variance for population statistics, including the mean and the standard deviation.
- Applicable to a wide range of population statistics where repeated omission of observations and recalculation is feasible.
Notes or pitfalls
Section titled “Notes or pitfalls”- Can be computationally intensive, especially for large datasets.
- Assumes observations are independent; this assumption may be violated in some real-world applications.
- Users should consider potential biases and limitations of the method when interpreting results.
Related terms
Section titled “Related terms”- Bias
- Variance
- Estimator
- Mean
- Standard deviation
- Observations