Jackknifemenetelmässä

Jackknifemenetelmässä, often referred to as the jackknife method, is a resampling statistical technique used to estimate the bias of a statistic and its variance. It is a non-parametric method, meaning it does not rely on assumptions about the underlying distribution of the data. The core idea behind the jackknife is to systematically remove one observation at a time from the dataset and recompute the statistic of interest.

To apply the jackknife method, a dataset of size n is considered. For each observation, a "replicate" dataset is created by excluding that single observation. This results in n replicate datasets, each of size n-1. The statistic of interest is then calculated for each of these n replicate datasets.

The bias of the statistic can be estimated by comparing the average of the statistics calculated from the replicate datasets to the statistic calculated from the original full dataset. The variance of the statistic can be estimated using the variability of the statistics calculated from the replicate datasets. Specifically, the variance is often estimated based on the differences between the replicate statistics and their mean.

The jackknife method is particularly useful when the analytical form of the bias or variance of a statistic is difficult or impossible to derive. It is widely used in various fields, including econometrics, machine learning, and survey analysis, for its robustness and ability to provide reliable estimates of uncertainty. It is a foundational technique in the broader family of resampling methods, which also includes the bootstrap.