Article
MSC:
60G10,
60G25,
60G40,
60K05,
62G05,
62M10 | MR 3301776 | Zbl 1308.62067 | DOI: 10.14736/kyb-2014-6-0869
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Keywords:
nonparametric estimation; stationary processes
nonparametric estimation; stationary processes
Summary:
For a binary stationary time series define $\sigma_n$ to be the number of consecutive ones up to the first zero encountered after time $n$, and consider the problem of estimating the conditional distribution and conditional expectation of $\sigma_n$ after one has observed the first $n$ outputs. We present a sequence of stopping times and universal estimators for these quantities which are pointwise consistent for all ergodic binary stationary processes. In case the process is a renewal process with zero the renewal state the stopping times along which we estimate have density one.
References:
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