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统计理论与建模：纪念 David Cox 爵士AI 解读

Part 1 Statistical theory - theoretical concepts significance tests theory of optimal tests estimation asymptotic theory. Part 2 Applied statistics - preliminary considerations statistical models statistical inference model adequancy exploratory and robust methods multi-variate methods use of computers. Part 3 Generalized linear models - a class of non-linear regression models likelihood functions estimation analysis of deviance checking the model. Part 4 Residuals and…

重抽样方法中的鞍点近似AI 解读

Saddlepoint approximations are shown to be easy to use and accurate in a variety of simple bootstrap and randomization applications. Examples include mean estimation, ratio estimation, two-sample comparisons, and autoregressive estimation.

Bootstrap 方法AI 解读

SUMMARY A survey of some developments in bootstrap methodology is given. Topics include confidence limits, significance tests, empirical likelihoods, conditioning, double bootstrapping, and numerical techniques. Special attention is given to regression problems. There are brief remarks about more complex problems, including variance component problems, time series and nonparametric regression.

重抽样方法中的鞍点近似AI 解读

Saddlepoint approximations are shown to be easy to use and accurate in a variety of simple bootstrap and randomization applications. Examples include mean estimation, ratio estimation, two-sample comparisons, and autoregressive estimation.

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最大似然估计精度的评估：观测与期望Fisher信息AI 解读

This paper concerns normal approximations to the distribution of the maximum likelihood estimator in one-parameter families. The traditional variance approximation is 1/§, where θ is the maximum likelihood estimator and § is the expected total Fisher information. Many writers, including R. A. Fisher, have argued in favour of the variance estimate 1/I(x), where I(x) is the observed information, i.e. minus the second derivative of the log likelihood function at θ given data x.…

位置与尺度参数的似然推断AI 解读

We obtain a normal approximation to the conditional distribution of maximum likelihood estimates in location-scale families. The covariance matrix is the inverse of minus the observed log likelihood second derivative matrix at the likelihood maximum, as opposed to the inverse of Fisher information, to which it is superior. Confidence intervals for the location parameter are discussed. Small sample numerical results are given for the Cauchy case to illustrate the accuracy of…

改进 Jackknife：以相关系数估计为重点AI 解读

Second-order asymptotic properties of the jackknife procedure are discussed, and the jackknifed estimator is shown to be a vulnerable estimator whose variation can be severely underestimated by the jackknife standard error. Simple robust alternatives to the average pseudovalue are discussed. Particular emphasis is placed on estimation of a correlation coefficient. Numerical examples are given.

最大似然估计精度评估：观测与期望 Fisher 信息AI 解读

This paper concerns normal approximations to the distribution of the maximum likelihood estimator in one-parameter families. The traditional variance approximation is 1/§, where θ is the maximum likelihood estimator and § is the expected total Fisher information. Many writers, including R. A. Fisher, have argued in favour of the variance estimate 1/I(x), where I(x) is the observed information, i.e. minus the second derivative of the log likelihood function at θ given data x.…

改进 Jackknife：重点讨论相关系数估计AI 解读

Second-order asymptotic properties of the jackknife procedure are discussed, and the jackknifed estimator is shown to be a vulnerable estimator whose variation can be severely underestimated by the jackknife standard error. Simple robust alternatives to the average pseudovalue are discussed. Particular emphasis is placed on estimation of a correlation coefficient. Numerical examples are given.

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两段线性回归中的推断AI 解读

Procedures are outlined for obtaining maximum likelihood estimates and likelihood confidence regions in the intersecting two-phase linear regression model. The procedures are illustrated on a small set of data, and the distributional properties are examined empirically.

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随机变量序列中变点位置的推断AI 解读

Inference is considered about the point in a sequence of random variables at which the probability distribution changes. In particular, we examine a normal distribution with changing mean. The asymptotic distribution of the maximum likelihood estimate is derived and also the asymptotic distribution of the likelihood ratio statistic for testing hypotheses about the change-point. These asymptotic distributions are compared with some finite sample empirical distributions.

二项变量序列中变点的统计推断AI 解读

The problem of making inferences about the point in a sequence of zero-one variables at which the binomial parameter changes is considered. The asymptotic distribution of the maximum likelihood estimate of the change-point is derived in computable form using random walk- results. The asymptotic distributions of likelihood ratio statistics for testing hypothesis about the change-point are also obtained. Some exact numerical results for these asymptotic distributions are given…