Publication

Correcting Jackknife Confidence Intervals

1998
Reports

Abstract

This paper presents a method for constructing confidence intervals using the jackknife. Asymptotic expansions are used to assess and reduce the skewness. It is proved that, although the error in the coverage rate remains of order O(1/n) for two-sided intervals, the main term due to the skewness in the distribution is eliminated, which constitute an improvement to the normal approximation that is important in the context of small samples. Several simulations are presented, with different distributions and functionals, and compared to the empirical accuracy obtained with a normal approximation. It is observed that our method produces in many cases a better empirical accuracy than the intervals due to a normal approximation, without requiring any knowledge on the underlying distribution.

Official source

https://infoscience.epfl.ch/entities/publication/ad3390f1-b17f-4a0e-9ae7-e84c15ff5f54

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1998
Reports

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ad3390f1-b17f-4a0e-9ae7-e84c15ff5f54

About this result

Related concepts (32)

Confidence interval

In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level, degree of confidence or confidence coefficient represents the long-run proportion of CIs (at the given confidence level) that theoretically contain the true value of the parameter; this is tantamount to the nominal coverage probability.

Normal distribution

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.

Tolerance interval

A tolerance interval (TI) is a statistical interval within which, with some confidence level, a specified sampled proportion of a population falls. "More specifically, a 100×p%/100×(1−α) tolerance interval provides limits within which at least a certain proportion (p) of the population falls with a given level of confidence (1−α)." "A (p, 1−α) tolerance interval (TI) based on a sample is constructed so that it would include at least a proportion p of the sampled population with confidence 1−α; such a TI is usually referred to as p-content − (1−α) coverage TI.

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Correcting Jackknife Confidence Intervals

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