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- W2023558114 abstract "ABSTRACT Nonstandard mixtures are those that result from a mixture of a discrete and a continuous random variable. They arise in practice, for example, in medical studies of exposure. Here, a random variable that models exposure might have a discrete mass point at no exposure, but otherwise may be continuous. In this article we explore estimating the distribution function associated with such a random variable from a nonparametric viewpoint. We assume that the locations of the discrete mass points are known so that we will be able to apply a classical nonparametric smoothing approach to the problem. The proposed estimator is a mixture of an empirical distribution function and a kernel estimate of a distribution function. A simple theoretical argument reveals that existing bandwidth selection algorithms can be applied to the smooth component of this estimator as well. The proposed approach is applied to two example sets of data. Keywords: AuditingBandwidth estimationEmpirical distribution functionExposure dataKernelPlug-in estimateMathematics Subject Classification: Primary 62G07Secondary 62G30" @default.
- W2023558114 created "2016-06-24" @default.
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- W2023558114 date "2005-08-01" @default.
- W2023558114 modified "2023-10-06" @default.
- W2023558114 title "Nonparametric Estimation of Distribution Functions of Nonstandard Mixtures" @default.
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- W2023558114 doi "https://doi.org/10.1081/sta-200066353" @default.
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