The nonparametric two-sample bootstrap is applied to computing uncertainties of measures in receiver operating characteristic (ROC) analysis on large datasets in areas such as biometrics, speaker recognition, etc. when the analytical method cannot be used. Its validation was studied by computing the standard errors of the area under ROC curve using the well-established analytical Mann–Whitney statistic method and also using the bootstrap. The analytical result is unique. The bootstrap results are expressed as a probability distribution due to its stochastic nature. The comparisons were carried out using relative errors and hypothesis testing. These match very well. This validation provides a sound foundation for such computations. 相似文献
In nonregular problems where the conventional \(n\) out of \(n\) bootstrap is inconsistent, the \(m\) out of \(n\) bootstrap provides a useful remedy to restore consistency. Conventionally, optimal choice of the bootstrap sample size \(m\) is taken to be the minimiser of a frequentist error measure, estimation of which has posed a major difficulty hindering practical application of the \(m\) out of \(n\) bootstrap method. Relatively little attention has been paid to a stronger, stochastic, version of the optimal bootstrap sample size, defined as the minimiser of an error measure calculated directly from the observed sample. Motivated by this stronger notion of optimality, we develop procedures for calculating the stochastically optimal value of \(m\). Our procedures are shown to work under special forms of Edgeworth-type expansions which are typically satisfied by statistics of the shrinkage type. Theoretical and empirical properties of our methods are illustrated with three examples, namely the James–Stein estimator, the ridge regression estimator and the post-model-selection regression estimator. 相似文献
As China’s economy is rapidly changing from a planned to a capitalist economy, many families find themselves financially struggling. In some cases, conflicting values and attitudes may contribute to mental health challenges such as depression that would lead to further feelings of helplessness and immobilization. Using a random sample of 1006 low-income households from Pudong District of Shanghai, China, this study aims to examine the relationships between household assets, beliefs about government as the primary way to improve economic circumstances and self-reported depressive symptoms. In addition, this study investigates the mediation effects of beliefs that government is the best change agent for improved life circumstances on the relationship between household assets and depression. We found those who indicated that government was the main means for attaining a better life had significantly higher depression levels whereas higher numbers of household assets were associated with lower depression levels. We also found that viewing government as the most important change agent only partially mediated the relationship between household assets and depression (p?<?.001). Findings from this study support anti-poverty policies and social work related practice initiatives aimed at assisting low income families in China, in particular the need to address psychological as well as economic needs.