Contents
How do you find the exact confidence interval?
To find an exact confidence interval, one need to know the distribution of the population to find out the sampling distribution of the statistic used to estimate the parameter. Once you know the sampling distribution of the statistic, you can construct the interval.
How does Standard Deviation affect confidence interval?
As the sample size increases, the standard deviation of the sampling distribution decreases and thus the width of the confidence interval, while holding constant the level of confidence.
Which is the best confidence interval for a quantile?
Besides the point estimate ^xp x ^ p we also would like to report a two-sided (1 −α)⋅ 100% ( 1 − α) ⋅ 100 % confidence interval (xl p,xu p) ( x p l, x p u) for the desired population quantile.
How to find confidence intervals for order statistics?
Restricting the limits of this confidence intervals to be one of the realisations from the order statistics implies that we need to find indices d d and e e with d < e d < e s.t. P (x(d) ≤ xp ≤ x(e)) ≥ 1−α. P ( x ( d) ≤ x p ≤ x ( e)) ≥ 1 − α. Note that it may not be possible to achieve the desired coverage exactly in this case.
When to use an interpolate argument for a quantile?
However, when the interpolate argument is set to TRUE (the default), an additional interpolation step between the two neighbouring order statistics is performed as suggested in the work of Nyblom (1992), which extends work for the median by Hettmansperger and Sheather (1986) to arbitrary quantiles. It generates intervals of the form:
Why is the preceding interval a conservative interval?
The preceding interval is conservative because the actual confidence level, given by the left-hand side of Equation (1), is greater than the specified value 1 − α. It is sometimes impossible to construct a distribution-free statistical interval that has at least the desired confidence level.