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中心化最小二乘预测交叉验证中的 Moore–Penrose 广义逆降更新AI 解读

SUMMARY Given a p × p symmetric matrix B and a p-vector c outside the range of B, a simple expression is formulated for the action of the Moore-Penrose generalized inverse B + on a vector b in the range of B, in terms of b, c and (B + cc‱)+. A special case of this formula gives a ‘downdating’ formula for the vector of least squares regression coefficients based on the Moore-Penrose inverse of the centred sum of squares and products matrix. The formula is analogous to that…

连续谱回归：以交叉验证统一最小二乘、偏最小二乘与主成分回归AI 解读

SUMMARY The paper addresses the evergreen problem of construction of regressors for use in least squares multiple regression. In the context of a general sequential procedure for doing this, it is shown that, with a particular objective criterion for the construction, the procedures of ordinary least squares and principal components regression occupy the opposite ends of a continuous spectrum, with partial least squares lying in between. There are two adjustable ‘parameters’…

不同批量下比例估计的刀切法、交叉验证法与经典方法AI 解读

Some properties of a proposed jackknife estimator of a proportion from batches of different sizes are exposed. Alternative ‘computer-intensive’ estimators are devised which, together with some ‘classical’ estimators, are then compared in a simulation study of their mean squared errors and the coverage and expected length of their associated confidence intervals.

信赖推断的函数模型基础AI 解读

The role of functional models and their associated fiducial analysis is explored in an attempt to uncover a general theory of fiducial inference.

交叉验证与 Akaike 准则选择模型的渐近等价性AI 解读

Summary A logarithmic assessment of the performance of a predicting density is found to lead to asymptotic equivalence of choice of model by cross-validation and Akaike's criterion, when maximum likelihood estimation is used within each model.

交叉验证的支持与反对：渐近分析AI 解读

The asymptotic consistency of cross-validatory assessment and the asymptotic efficiency of cross-validatory choice is investigated both in some generality and also in the context of particular applications.

经验概率测度的大偏差AI 解读

Sanov's statement of first-order asymptotic behaviour of probabilities of large deviations of an empirical distribution function is here established for empirical probability measures, with attendant simplification of conditions. For the case of distribution functions, our theorem is strictly more general than a specialisation of results of Hoadley.

交叉验证与多项类别预测AI 解读

The method of cross-validatory choice and assessment is applied to prediction of a multinomial indicator. The resulting predictor is compared with analogous expressions due to Good and Fienberg & Holland. Some numerical comparisons are made.

期望一致性与广义贝叶斯推断AI 解读

In a previous paper, the authors introduced a new criterion of expectation consistency between probability distributions of discrete data given discrete parameter values and arbitrary posterior probability distributions for the parameter. It is here shown, under very weak assumptions, that expectation consistency implies that the posterior distributions are generalized Bayes. However when the posterior distributions are generalized Bayes, the implied prior distribution need…

贝叶斯推断与结构推断中的边际化悖论AI 解读

Summary We describe a range of routine statistical problems in which marginal posterior distributions derived from improper prior measures are found to have an unBayesian property—one that could not occur if proper prior measures were employed. This paradoxical possibility is shown to have several facets that can be successfully analysed in the framework of a general group structure. The results cast a shadow on the uncritical use of improper prior measures. A separate…

常规统计问题中非正规先验贝叶斯推断的非贝叶斯后果AI 解读

For two routine statistical problems, inference about the ratio of two exponential means and inference about the coefficient of variation of a normal random variable, a serious pathology of Bayesian inference based on improper priors is uncovered and investigated.

摘要暂缺

常规统计问题中非正常先验贝叶斯推断的反贝叶斯后果AI 解读

For two routine statistical problems, inference about the ratio of two exponential means and inference about the coefficient of variation of a normal random variable, a serious pathology of Bayesian inference based on improper priors is uncovered and investigated.

不放回抽样的极端尾概率与两样本正态得分检验的精确 Bahadur 效率AI 解读

A theorem is stated for the asymptotic behaviour of the extreme tail probabilities of the distribution of the sample total or average in sampling without replacement from a wide class of populations. The theorem is applied to asymptotically normal populations, yielding the exact Bahadur efficiency of the normal scores test.

不放回抽样的极端尾概率与两样本正态得分检验的精确 Bahadur 效率AI 解读

A theorem is stated for the asymptotic behaviour of the extreme tail probabilities of the distribution of the sample total or average in sampling without replacement from a wide class of populations. The theorem is applied to asymptotically normal populations, yielding the exact Bahadur efficiency of the normal scores test.

双样本 Wilcoxon 统计量零假设分布的极端尾概率AI 解读

By a technique involving an envelope, the asymptotic behaviour of the extreme tail probabilities of the null distribution of the two-sample Wilcoxon statistic is examined and calculated. Application is made to an efficiency comparison with the normal test.

摘要暂缺