Quenouille (1949) invented the jackknife technique. The purpose of this was to reduce bias by looking at multiple samples of data in a methodical way. The name jackknife seems to have been coined by the well-known statistician John W. Tukey. Due mainly to the lack of computational power, the advances and utility of the jackknife method were restricted. Efron invented the bootstrap method in 1979 (see the following section for its applications) and established the connection with the jackknife method. In fact, these two methods have a lot in common and are generally put under the umbrella of resampling methods.

Suppose that we draw a random sample of size n from a probability distribution F, and we denote by the parameter of interest. Let be an estimator of , and here we don't have the probability distribution of for a given . Resampling methods will help in carrying out statistical inference when the probability distribution is unknown. A formal definition of the concept is in order.

Definition: Resampling methods are ways of estimating the bias and variance of the estimator that uses the values of based on subsamples from the available observations .

The jackknife technique is a resampling method, and we will lay down its general procedure in the ensuing discussion. As stated previously, is an estimator of . For simplicity, we define the vector of the given observations by . The important quantity in setting up this procedure is the pseudovalue, and we will define this mathematically next.

Definition: Let , that is, is the vector without the i-th observation. The i-th pseudovalue of is then defined as follows:

It can be mathematically demonstrated that the pseudovalue is equivalent to the following:

Thus, the pseudovalue is seen as the bias-corrected version of . The pseudovalues defined here are also referred to as delete-one jackknife. The jackknife method treats the pseudovalues as independent observations with mean , and then applies the central limit theorem for carrying out the statistical inference. The mean and (sampling) variance of the pseudovalues is given as follows: