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参照样本集合对频率学推断的影响AI 解读

We employ second-order likelihood asymptotics to investigate how ideal frequentist inferences depend on the probability model for the data through more than the likelihood function, referring to this as the effect of the reference set. There are two aspects of higherorder corrections to first-order likelihood methods, namely (i) that involving effects of fitting nuisance parameters and leading to the modified profile likelihood, and (ii) another part pertaining to limitation…

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高阶渐近理论与似然原则：单参数模型AI 解读

Inferences based on higher-order asymptotics, in contrast to those based on standard first-order methods, approximate exact inferences closely enough to depend on the reference set. We use this feature to quantify the effect of the reference set on exact inferences. In particular, the difference in P-values for two reference sets can be at most O(n−½), and it is seen that one can often identify the coefficient of n−½. Although this is useful from a foundational viewpoint,…

多参数指数族中高阶渐近方法的实践应用AI 解读

SUMMARY Recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families, especially in generalized linear models. The aim here is to clarify and explore these. Attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family. Excellent approximations to exact conditional inferences are often…

测量误差问题：原子弹幸存者辐射剂量反应分析的启示AI 解读

Some basic issues in the errors-in-variables problem are discussed, in terms of considerations that arose in analyses of radiation effects on atomic bomb survivors. The setting essentially involves generalized linear models for the response variables, a very nonnormal distribution of the true covariable, and multiplicative errors in the observed covariable. Consideration is given to distinctions between structural and functional modeling. It is argued that careful attention…

广义线性模型中的残差AI 解读

Generalized linear models are regression-type models for data not normally distributed, appropriately fitted by maximum likelihood rather than least squares. Typical examples are models for binomial or Poisson data, with a linear regression model for a given, ordinarily nonlinear, function of the expected values of the observations. Use of such models has become very common in recent years, and there is a clear need to study the issue of appropriate residuals to be used for…

It is shown that any test of normality computed from autoregressive residuals has the same limiting null distribution as for the standard case of independent, identically distributed observations with estimated parameters. Some numerical results are given to indicate that this approximation is acceptable for sample size 20 in first- and second-order models. Limited numerical results are also given to explore the effect of incorrectly specifying the order.

删失生存数据的拟合优度检验AI 解读

The problem of testing the underlying distribution in a general regression model is considered when the data are right censored. It is proposed that tests be based on efficient scores from a certain class of parametric alternatives. The connection between tests based on the scores and more traditional approaches using empirical distribution functions is explored. Neyman's smooth test is extended to allow for censored data.

自回归模型中的正态性检验AI 解读

It is shown that any test of normality computed from autoregressive residuals has the same limiting null distribution as for the standard case of independent, identically distributed observations with estimated parameters. Some numerical results are given to indicate that this approximation is acceptable for sample size 20 in first- and second-order models. Limited numerical results are also given to explore the effect of incorrectly specifying the order.

分组生存数据中 Cox 模型估计回归参数的效率AI 解读

The efficiency of nonparametric survival analysis (Cox, 1972, 1975) relative to parametric analysis is examined for grouped data. This setting avoids the difficulties of partial likelihood and allows standard likelihood methods to apply. The results obtained here are similar to published results for ungrouped data, but are perhaps more easily understood. Some insight is also gained for problems involving time-dependent covariables and for problems with many covariables.

某些统计量中以估计量替代参数的渐近影响AI 解读

In a variety of statistical problems, one is interested in the limiting distribution of statistics $\hat{T}_n = T_n(y_1, y_2, \cdots, y_n; \hat{\lambda}_n)$, where $\hat{\lambda}_n$ is an estimator of a parameter in the distribution of the $y_i$ and where the limiting distribution of $T_n = T_n(y_1, y_2, \cdots, y_n; \lambda)$ is relatively easy to find. For cases in which the limiting distribution of $T_n$ is normal with mean independent of $\lambda$, a useful method is…

分组生存数据中 Cox 模型回归参数估计的效率AI 解读

The efficiency of nonparametric survival analysis (Cox, 1972, 1975) relative to parametric analysis is examined for grouped data. This setting avoids the difficulties of partial likelihood and allows standard likelihood methods to apply. The results obtained here are similar to published results for ungrouped data, but are perhaps more easily understood. Some insight is also gained for problems involving time-dependent covariables and for problems with many covariables.

回归模型误差正态性的检验AI 解读

It was shown by Pierce & Kopecky (1979) that tests of normality appropriate for the identically distributed case are asymptotically valid when computed from residuals in regression situations. Numerical results based on simulation are given here to study the adequacy of this result for sample sizes of 20 and 40. The Shapiro-Wilk and Anderson-Darling tests are found to be quite adequate for n = 20 in typical simple linear regression situations, and for n = 40 in certain…

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复合假设下的 Neyman 光滑拟合优度检验AI 解读

A method is given for adjustment of the Neyman smooth goodness-of-fit test to allow for estimation of parameters in a composite hypothesis. With this method the limiting distribution under the hypothesis is chi-squared, in contrast to a method given by Barton for this problem. The basis of the method is a standard modification of the quadratic score statistic.

光滑拟合优度检验的效率AI 解读

The smooth goodness-of-fit test of Neyman (1937) was generalized to composite hypotheses by Javitz (1975) and Thomas and Pierce (1979). The test statistic is derived, as is its local asymptotic relative efficiency (LARE), which permits its comparison with other quadratic score statistic (QSS) tests, which include a Pearson-type χ2 test. For testing the negative exponential and normal distributions, the smooth test is seen to have greater LARE than the Pearson-type test and…

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回归模型误差分布的拟合优度检验AI 解读

Asymptotic results are given for the problem of testing goodness of fit for any specified distribution of errors in multiple regression models. In particular, the results apply to the case of testing for normality in standard regression and experimental design models. For a very wide class of goodness of fit statistics, in particular those which depend only on the empirical distribution of the residuals, it is shown that the limiting distributions under the null hypothesis…

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用于计算机辅助疾病鉴别诊断的离散多元密度估计AI 解读

A Bayesian approach is taken to the problem of estimating a multivariate discrete density. Prior distributions on the space of multivariate densities are formulated to reflect the idea that the density is near a particular one, or near one which has independent variates. Given a sample of multivariate observations, an approximation to the posterior distribution of the unknown density is developed, and simple formulae for a density which approximates the mode of this…

Weibull 分布的贝叶斯—信 fiducial 推断AI 解读

Procedures are developed for specifying confidence intervals, from possibly censored data, for any characteristic of a two-parameter Weibull population. Although the methods are formally Bayesian, they have exact relative frequency interpretation for uncensored and Type II censored data. Some simulation results are given to indicate relative frequency behavior for Type 1 censoring, and for comparison to other methods.

频率学派推断理论中的若干困难AI 解读

A study of relationships between confidence regions being Bayesian, and the existence of some generalizations of Fisher's notion of relevant subsets. For a betting scheme introduced by Buehler, and for finite parameter space, it is shown that non-Bayesian procedures allow a winning strategy for a statistician's adversary. It is further shown, for finite parameter space, non-Bayesian procedures must admit conditional confidence levels bounded away from the unconditional…