کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1148366 | 957831 | 2009 | 14 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A frequentist understanding of sets of measures A frequentist understanding of sets of measures](/preview/png/1148366.png)
We present a mathematical theory of objective, frequentist chance phenomena that uses as a model a set of probability measures. In this work, sets of measures are not viewed as a statistical compound hypothesis or as a tool for modeling imprecise subjective behavior. Instead we use sets of measures to model stable (although not stationary in the traditional stochastic sense) physical sources of finite time series data that have highly irregular behavior. Such models give a coarse-grained picture of the phenomena, keeping track of the range of the possible probabilities of the events. We present methods to simulate finite data sequences coming from a source modeled by a set of probability measures, and to estimate the model from finite time series data. The estimation of the set of probability measures is based on the analysis of a set of relative frequencies of events taken along subsequences selected by a collection of rules. In particular, we provide a universal methodology for finding a family of subsequence selection rules that can estimate any set of probability measures with high probability.
Journal: Journal of Statistical Planning and Inference - Volume 139, Issue 6, 1 June 2009, Pages 1879–1892