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向量参数的高精度方向推断AI 解读

We consider statistical inference for a vector-valued parameter of interest in a regular asymptotic model with a finite-dimensional nuisance parameter. We use highly accurate likelihood theory to derive a directional test, in which the |$p$|-value is obtained by one-dimensional numerical integration. This extends the results of Davison et al. (2014) for linear exponential families to nonlinear parameters of interest and to more general models. Examples and simulations…

线性指数族中向量参数的精确方向性推断AI 解读

We consider inference on a vector-valued parameter of interest in a linear exponential family, in the presence of a finite-dimensional nuisance parameter. Based on higher-order asymptotic theory for likelihood, we propose a directional test whose p-value is computed using one-dimensional integration. The work simplifies and develops earlier research on directional tests for continuous models and on higher-order inference for discrete models, and the examples include…

用于贝叶斯与频率学派推断的默认先验AI 解读

Summary We investigate the choice of default priors for use with likelihood for Bayesian and frequentist inference. Such a prior is a density or relative density that weights an observed likelihood function, leading to the elimination of parameters that are not of interest and then a density-type assessment for a parameter of interest. For independent responses from a continuous model, we develop a prior for the full parameter that is closely linked to the original Bayes…

平均对数似然与高阶近似AI 解读

Higher-order approximations to p-values can be obtained from the loglikelihood function and a reparameterization that can be viewed as a canonical parameter in an exponential family approximation to the model. This approach clarifies the connection between Skovgaard (1996) and Fraser et al. (1999a), and shows that the Skovgaard approximation can be obtained directly using the mean loglikelihood function.

离散数据的改进似然推断AI 解读

Summary Discrete data, particularly count and contingency table data, are typically analysed by using methods that are accurate to first order, such as normal approximations for maximum likelihood estimators. By contrast continuous data can quite generally be analysed by using third-order procedures, with major improvements in accuracy and with intrinsic separation of information concerning parameter components. The paper extends these higher order results to discrete data,…

关于由边际密度构造伪似然的说明AI 解读

For likelihood‐based inference involving distributions in which high‐dimensional dependencies are present it may be useful to use approximate likelihoods based, for example, on the univariate or bivariate marginal distributions. The asymptotic properties of formal maximum likelihood estimators in such cases are outlined. In particular, applications in which only a single q×1 vector of observations is observed are examined. Conditions under which consistent estimators of…

渐近分析与统计推断理论AI 解读

Asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable. More importantly, asymptotic analysis can also provide insight into the inference process itself, suggesting what information is available and how this information may be extracted. The development of likelihood inference over the past twenty-some years provides an illustration of the interplay between techniques of approximation and…

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通常似然与调整似然所对应的置信区间AI 解读

Summary In the presence of nuisance parameters, we drive an explicit higher order asymptotic formula to compare the expected lengths of confidence intervals given by likelihood ratio statistics arising from the usual profile likelihood and various adjustments thereof. Highest posterior density regions, with approximate frequentist validity, are also included in the study.

指数模型的多参数检验：基于似然的三阶近似AI 解读

For composite testing of several canonical components in an exponential model, a conical or directional test provides a one-dimensional measure of departure. We approximate the distribution of this test statistic to third order by numerical inversion of a profile likelihood. The method extends the Lugannani & Rice type formula to kernels other than the normal.

指数模型的多参数检验：基于似然的三阶近似AI 解读

For composite testing of several canonical components in an exponential model, a conical or directional test provides a one-dimensional measure of departure. We approximate the distribution of this test statistic to third order by numerical inversion of a profile likelihood. The method extends the Lugannani & Rice type formula to kernels other than the normal.

调整剖面似然计算的一则说明AI 解读

SUMMARY An adjustment to the profile likelihood examined by Cox and Reid required orthogonalization of the nuisance parameters with respect to the parameter of interest. An approximation to the adjusted profile likelihood not requiring explicit orthogonalization is derived and exemplified.

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剖面似然与修正剖面似然差异札记AI 解读

The difference between profile likelihood and modified profile likelihood depends primarily on the expected value of a certain third order derivative of the log likelihood. It is shown that in exponential family problems this derivative vanishes if the parameter of interest is a mean parameter but in general not when it is a canonical parameter. As examples some matched pair problems for exponential family models are considered.

非正态线性回归：高维显著性水平计算的一个例子AI 解读

Analysis of nonnormal linear models leads to an initial conditioning on the standardized residuals, giving an unnormed density on Rk, where k is the number of parameters. To obtain an observed level of significance for a single parameter it is then necessary to calculate a marginal probability, thus requiring integration in k dimensions. In this paper a conditional approach to evaluating the observed level of significance is developed, and an importance sampling technique is…

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非正态线性回归：高维显著性水平的一个例子AI 解读

Analysis of nonnormal linear models leads to an initial conditioning on the standardized residuals, giving an unnormed density on Rk, where k is the number of parameters. To obtain an observed level of significance for a single parameter it is then necessary to calculate a marginal probability, thus requiring integration in k dimensions. In this paper a conditional approach to evaluating the observed level of significance is developed, and an importance sampling technique is…

剖面似然的调整AI 解读

Conditional and marginal likelihoods constructed from parameter-dependent functions of the data have an additional parameter dependence that changes with the choice of supporting metric for the corresponding densities. We consider constructing marginal and conditional likelihoods by using densities expressed in terms of an instrinsic choice of support measure, based on either Euclidean metric or the constant information metric. Barndorff-Nielsen's (1983) approximation to the…

近似条件似然的一个时间序列例证AI 解读

We consider the calculation of confidence intervals for the correlation parameter, based on observations of a large number of short Gaussian first-order autoregressive processes with different means but common correlation and variance. Ordinary profile likelihood gives very misleading answers. The approximate conditional likelihood of Cox & Reid (1987) is calculated and shown to lead to consistent estimation of the correlation. Simulations verify that the usual asymptotic…

剖面似然的调整AI 解读

Conditional and marginal likelihoods constructed from parameter-dependent functions of the data have an additional parameter dependence that changes with the choice of supporting metric for the corresponding densities. We consider constructing marginal and conditional likelihoods by using densities expressed in terms of an instrinsic choice of support measure, based on either Euclidean metric or the constant information metric. Barndorff-Nielsen's (1983) approximation to the…

近似条件似然的一个时间序列示例AI 解读

We consider the calculation of confidence intervals for the correlation parameter, based on observations of a large number of short Gaussian first-order autoregressive processes with different means but common correlation and variance. Ordinary profile likelihood gives very misleading answers. The approximate conditional likelihood of Cox & Reid (1987) is calculated and shown to lead to consistent estimation of the correlation. Simulations verify that the usual asymptotic…

实参数的条件推断：样本空间上的微分方法AI 解读

A one-dimensional conditional procedure defines a partition of the sample space into curves which can be represented by means of a unit vector field. A formula is given for the conditional distribution in terms of local properties of the vector field. Conditions are developed for reducing the first-order effects of nuisance parameters and reproducing to higher order the likelihood change for the parameter of interest. The emphasis is on extending exponential family methods…

实参数的条件推断：样本空间上的微分方法AI 解读

A one-dimensional conditional procedure defines a partition of the sample space into curves which can be represented by means of a unit vector field. A formula is given for the conditional distribution in terms of local properties of the vector field. Conditions are developed for reducing the first-order effects of nuisance parameters and reproducing to higher order the likelihood change for the parameter of interest. The emphasis is on extending exponential family methods…