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The Estimation of a Location Parameter When the Scale Parameter is Confined to a Finite Range: The Notion of a Generalized Ancillary Statistic

尺度参数限于有限范围时的位置估计与广义辅助统计量

The estimation of the location parameter θ in a location-scale model is considered when the scale parameter σ is confined to a finite range. The application to robustness considerations and some implications for conditional inference are discussed.

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The estimation of a location parameter when the scale parameter is confined to a finite range: The notion of a generalized ancillary statistic

尺度参数限于有限范围时的位置估计:广义辅助统计量

The estimation of the location parameter θ in a location-scale model is considered when the scale parameter σ is confined to a finite range. The application to robustness considerations and some implications for conditional inference are discussed.

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The Generalised Problem of the Nile: Robust Confidence Sets for Parametric Functions

广义尼罗河问题:参数函数的稳健置信集

The pivotal model is described and applied to the estimation of parametric functions $\phi(\theta)$. This leads to equations of the form $H(x; \theta) = G\{p(x, \theta)\}$. These can be solved directly or by the use of differential equations. Examples include various parametric functions $\phi(\theta, \sigma)$ in a general location-scale distribution $f(p), p = (x - \theta)/\sigma$ and in two location-scale distributions. The latter case includes the ratio of the two scale…

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Normal likelihoods and their relation to large sample theory of estimation

正态形似然及其与大样本估计理论的关系

Normal likelihoods are shown to be associated with asymptotic normal distributions of large sample theory. An examination of the likelihood function can indicate when standard large sample theory of estimation can be applied and when it may be inaccurate and misleading to do so. Transformations that improve the accuracy and so extend the domain of application of asymptotic methods can sometimes be suggested by their effect on the likelihood function. An examination of the…

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Application of Likelihood Methods to Models Involving Large Numbers of Parameters

似然方法在含大量参数模型中的应用

J. D. Kalbfleisch, D. A. Sprott; Application of Likelihood Methods to Models Involving Large Numbers of Parameters, Journal of the Royal Statistical Societ

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Application of Likelihood Methods to Models Involving Large Numbers of Parameters

似然方法在含大量参数模型中的应用

Summary Likelihood methods of dealing with some multiparameter problems are introduced and exemplified. Specifically, methods of eliminating nuisance parameters from the likelihood function so that inferences can be made about the parameters of interest are considered. In this regard integrated likelihoods, maximum relative likelihoods, conditional likelihoods, marginal likelihoods and second-order likelihoods are introduced and their uses illustrated in examples. Marginal…

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Examples of Likelihoods and Comparison with Point Estimates and Large Sample Approximations

似然函数实例及其与点估计和大样本近似的比较

The exact likelihood functions are examined for several examples of data chosen from the literature. These are compared with the likelihoods arising from the large sample approximations and with point estimates that were actually used in the literature. It is concluded that large sample approximations (application of standard maximum likelihood theory) can be misleading for inferences and should be checked against the actual likelihood functions. Similarly point estimates…

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Examples of Likelihoods and Comparison with Point Estimates and Large Sample Approximations

似然实例及其与点估计和大样本近似的比较

The exact likelihood functions are examined for several examples of data chosen from the literature. These are compared with the likelihoods arising from the large sample approximations and with point estimates that were actually used in the literature. It is concluded that large sample approximations (application of standard maximum likelihood theory) can be misleading for inferences and should be checked against the actual likelihood functions. Similarly point estimates…

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