Jackknife Estimation

Jackknife estimation recomputes a statistic with each observation left out in turn and uses the spread and average of these leave-one-out values to estimate the statistic's bias and standard error.

잭나이프 추정은 관측을 하나씩 빼고 통계량을 다시 계산한 값들로 원래 통계량의 편향과 표준오차를 추정하는 재표집 방법이다.

How can I estimate the bias and standard error of a statistic without a formula?

공식이 없는 통계량의 편향과 표준오차는 어떻게 추정하나요?

The jackknife computes the statistic n times, each time omitting one observation, and estimates bias as (n − 1) times the difference between the mean leave-one-out value and the full-sample value. Its standard error is a scaled spread of the leave-one-out values, and it is exact for the sample mean.

When to use Jackknife Estimation

• You need a quick, deterministic bias and standard-error estimate
• The statistic is a smooth function such as a mean, variance or ratio
• You want to compute the acceleration constant for a BCa interval

When to use something else

• The statistic is non-smooth, such as a median or quantile; use the bootstrap instead
• Observations are clustered or dependent; use a cluster jackknife or block bootstrap instead

Assumptions and requirements

• Observations are independent
• The statistic changes smoothly when one observation is removed

What the analysis reports

• Estimates of mean, median, SD and variance
• Jackknife bias and bias-corrected estimates
• Jackknife standard errors
• t-based intervals

How to report it

The jackknife estimate of the [statistic] was [value] (bias = [value], SE = [value]).

Related methods

• Bootstrap Confidence Intervals (BCa)
• Robust Location and Scale Estimates

Run Jackknife Estimation on Quorant