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用马尔可夫链片段近似不完整函数数据AI 解读

We consider curve extension and linear prediction for functional data observed only on a part of their domain, in the form of fragments. We suggest an approach based on a combination of Markov chains and nonparametric smoothing techniques, which enables us to extend the observed fragments and construct approximated prediction intervals around them, construct mean and covariance function estimators, and derive a linear predictor. The procedure is illustrated on real and…

考虑稀释效应的组检测数据非参数方法AI 解读

Group testing methods are used widely to assess the presence of a contaminant, based on measurements of the concentration of a biomarker, for example to test the presence of a disease in pooled blood samples. The test would be perfect if it produced a positive result whenever the contaminant was present, and a negative result otherwise. However, in practice the test is always at least somewhat imperfect, for example because it is sensitive to the proportion of contaminated…

单变量与多变量群组检测数据的非参数及半参数回归新方法AI 解读

We consider nonparametric and semiparametric estimation of a conditional probability curve in the case of group testing data, where the individuals are pooled randomly into groups and only the pooled data are available. We derive a nonparametric weighted estimator that has optimality properties accounting for group sizes, and show how to extend it to multivariate settings, including the partially linear model. In the group testing context, it is natural to assume that the…

受噪声污染样本中密度导数平方积分的估计AI 解读

Summary We propose a kernel estimator of integrated squared density derivatives, from a sample that has been contaminated by random noise. We derive asymptotic expressions for the bias and the variance of the estimator and show that the squared bias term dominates the variance term. This coincides with results that are available for non-contaminated observations. We then discuss the selection of the bandwidth parameter when estimating integrated squared density derivatives…