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Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".
An example forest plot of five odds ratios (squares, proportional to weights used in meta-analysis), with the summary measure (centre line of diamond) and associated confidence intervals (lateral tips of diamond), and solid vertical line of no effect. Names of (fictional) studies are shown on the left, odds ratios and confidence intervals on ...
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.
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.
If the bootstrap distribution of an estimator is symmetric, then percentile confidence-interval are often used; such intervals are appropriate especially for median-unbiased estimators of minimum risk (with respect to an absolute loss function). Bias in the bootstrap distribution will lead to bias in the confidence interval.
The standard Gumbel distribution is the case where = and = with cumulative distribution function = ()and probability density function = (+).In this case the mode is 0, the median is ( ()), the mean is (the Euler–Mascheroni constant), and the standard deviation is /
Plotting the partial autocorrelation function and drawing the lines of the confidence interval is a common way to analyze the order of an AR model. To evaluate the order, one examines the plot to find the lag after which the partial autocorrelations are all within the confidence interval. This lag is determined to likely be the AR model's order ...