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指数族中更准确的置信区间AI 解读

Fisher's theory of maximum likelihood estimation routinely provides approximate confidence intervals for a parameter of interest θ, the standard intervals θ ^ ± zασ ^ where θ ^ is the maximum likelihood estimator, ô is an estimate of standard error based on differentiation of the log likelihood function, and zα is a normal percentile point. Recent work has produced systems of better approximate confidence intervals, which look more like exact intervals when exact intervals…

经验似然可作 Bartlett 校正AI 解读

It is shown that, in a very general setting, the empirical likelihood method for constructing confidence intervals is Bartlett-correctable. This means that a simple adjustment for the expected value of log-likelihood ratio reduces coverage error to an extremely low $O(n^{-2})$, where $n$ denotes sample size. That fact makes empirical likelihood competitive with methods such as the bootstrap which are not Bartlett-correctable and which usually have coverage error of size $n^{-1}$…

Bootstrap 置信区间与 Bootstrap 近似AI 解读

The BCa bootstrap procedure (Efron 1987) for constructing parametric and nonparametric confidence intervals is considered. Like the bootstrap, this procedure can be applied to complicated problems in a wide range of situations. For models indexed by a scalar parameter θ with efficient estimator , the BCa procedure relies on the existence of a transformation g(·) such that () is approximately normally distributed with standard deviation 1 + ag(θ), although explicit knowledge…