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The probability density function (PDF) for the Wilson score interval, plus PDF s at interval bounds. Tail areas are equal. Since the interval is derived by solving from the normal approximation to the binomial, the Wilson score interval ( , + ) has the property of being guaranteed to obtain the same result as the equivalent z-test or chi-squared test.
This yields 1.15448, which is not in the interval between (3a 3 + b 3) / 4 and b 3). Hence, it is replaced by the midpoint m = −2.71449. We have f(m) = 3.93934, so we set a 4 = a 3 and b 4 = −2.71449. In the fifth iteration, inverse quadratic interpolation yields −3.45500, which lies in the required interval.
The method is as follows: Suppose you have p-values, sorted into order lowest-to-highest , …,, and their corresponding hypotheses , …, (null hypotheses). You want the FWER to be no higher than a certain pre-specified significance level.
In statistics, interval estimation is the use of sample data to estimate an interval of possible values of a parameter of interest. This is in contrast to point estimation, which gives a single value. [1] The most prevalent forms of interval estimation are confidence intervals (a frequentist method) and credible intervals (a Bayesian method). [2]
The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.
Basic bootstrap, [40] also known as the Reverse Percentile Interval. [42] The basic bootstrap is a simple scheme to construct the confidence interval: one simply takes the empirical quantiles from the bootstrap distribution of the parameter (see Davison and Hinkley 1997, equ. 5.6 p. 194):
The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval. For a strictly unimodal function with an extremum inside the interval, it will find that extremum, while for an interval containing multiple extrema (possibly including the interval boundaries), it will converge to one of them.
Schematic of Jackknife Resampling. In statistics, the jackknife (jackknife cross-validation) is a cross-validation technique and, therefore, a form of resampling.It is especially useful for bias and variance estimation.