Jackknifemenetelmä

Jackknifemenetelmä, commonly known as the jackknife method, is a resampling technique used in statistics to estimate the variance of a statistic and to construct confidence intervals. It is a widely used alternative to the bootstrap method and is particularly useful when the statistic's distribution is unknown or complex. The jackknife works by systematically omitting one observation at a time from a dataset and recalculating the statistic of interest for each reduced dataset. These recalculated statistics are called pseudovalues.

The core idea behind the jackknife method is to approximate the bias and variance of an estimator by examining how the estimator changes when individual data points are removed. If a statistic is calculated from a sample of size n, the jackknife method will generate n different versions of the statistic, each calculated from a sample of size n-1. By analyzing the variation among these n pseudovalues, one can estimate the standard error of the original statistic. The jackknife estimator for the variance is typically proportional to the sum of squared differences between the pseudovalues and their mean.

The jackknife method is known for its simplicity and computational efficiency. It is often easier to implement than the bootstrap for certain types of statistics. However, it can sometimes be less accurate than the bootstrap, especially for statistics that are highly sensitive to outliers or for estimating higher-order moments. Despite these limitations, the jackknife remains a valuable tool in statistical inference, offering a robust way to assess the uncertainty associated with estimated parameters.