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基于积分似然的似然比统计量AI 解读

An integrated likelihood depends only on the parameter of interest and the data, so it can be used as a standard likelihood function for likelihood-based inference. In this paper, the higher-order asymptotic properties of the signed integrated likelihood ratio statistic for a scalar parameter of interest are considered. These results are used to construct a modified integrated likelihood ratio statistic and to suggest a class of prior densities to use in forming the…

用于非贝叶斯推断的积分似然函数AI 解读

Consider a model with parameter θ = (ψ, λ), where ψ is the parameter of interest, and let L(ψ, λ) denote the likelihood function. One approach to likelihood inference for ψ is to use an integrated likelihood function, in which λ is eliminated from L(ψ, λ) by integrating with respect to a density function π(λ|ψ). The goal of this paper is to consider the problem of selecting π(λ|ψ) so that the resulting integrated likelihood function is useful for non-Bayesian likelihood…

Higher‐order approximations to the distribution of the likelihood ratio statistic are considered for a class of nonregular models in which the maximum likelihood estimator of the parameter of interest is asymptotically distributed according to an exponential, rather than a normal, distribution. Asymptotic behaviour of this type often arises when the boundary of the support of the distributions under consideration depends on θ. A modified likelihood ratio statistic is…

修正估计函数AI 解读

In a parametric model the maximum likelihood estimator of a parameter of interest ψ may be viewed as the solution to the equation l′p(ψ) = 0, where lp denotes the profile loglikelihood function. It is well known that the estimating function l′p(ψ) is not unbiased and that this bias can, in some cases, lead to poor estimates of ψ. An alternative approach is to use the modified profile likelihood function, or an approximation to the modified profile likelihood function, which…

离散情形下最大似然估计量条件分布的似然比近似AI 解读

The likelihood ratio approximation, also called Barndorff‐Nielsen's approximation and often denoted by p*, provides a highly accurate approximation to the conditional density of a maximum likelihood estimator Θ given an ancillary statistic. In this paper, the properties of p* are considered for the case in which the underlying random variables have a lattice distribution and Θ has a discrete, but not necessarily lattice, distribution. If Θ has a lattice distribution, then p*…