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条件统计推断与相关性的量化AI 解读

Summary We argue that it can be fruitful to take a predictive view on notions such as the precision of a point estimator and the confidence of an interval estimator in frequentist inference. This predictive approach has implications for conditional inference, because it immediately allows a quantification of the concept of relevance for conditional inference. Conditioning on an ancillary statistic makes inference more relevant in this sense, provided that the ancillary is a…

连续统回归并不总是连续AI 解读

SUMMARY Continuum regression (CR) is regression of a response y on that linear combination t γ of explanatory variables which maximizes r 2(y, t) var(t)γ, where γ is chosen from a continuum of candidates. CR includes several common methods as special cases: ordinary least squares, principal component regression, partial least squares and a modified ridge regression. We demonstrate that CR, despite its name, can yield a predictor that is a discontinuous function of γ and of…

抽样调查推断中的精度估计：方差估计量选择准则AI 解读

We advocate the 'mean squared error of predicted squared error' as a universal criterion for the choice between variance estimators in sample survey inference. The predictive nature of the measure rewards variance estimators adapted to the amount of information in the actual sample. This makes the new measure more satisfactory than the simpler mean squared error of the variance estimator. The criterion turns out to be the same for design-based as for model-based inference,…

连续体回归与岭回归AI 解读

SUMMARY We demonstrate the close relationship between first-factor continuum regression and standard ridge regression. The difference is that continuum regression inserts a scalar compensation factor for that part of the shrinkage in ridge regression that has no connection with tendencies towards collinearity. We interpret this to mean that first-factor continuum regression is preferable in principle to ridge regression if we want protection against near collinearity but do…

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部分状态聚合面板数据中潜在马尔可夫结构的检验AI 解读

SUMMARY For dichotomous longitudinal panel data assumed to have been generated by a Markov chain but with only one of its states identifiable, the likelihood ratio and related tests for underlying Markovian structure are studied. It is shown that the likelihood ratio may be written as a product of conditionally independent likelihood ratios for testing independence in certain contingency tables, given margins. The tests are illustrated on data from malaria and…