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- W2023926812 abstract "Let $T subseteq I$ be sets of real numbers. Let ${Y(t): tin I}$ be a real time series whose covariance kernel is assumed known and positive definite. The mean is assumed either to be known or to be an unknown member of a known class of functions on $I$. For each fixed $sin I, Y(s)$ is predicted by a minimum mean square error unbiased linear predictor $hat{Y}(s)$ based on ${Y(t): tin T}$. If $hat{y}(s)$ is the evaluation of $hat{Y}(s)$ given that the sample path for ${Y(t): tin T}$ is an unknown element of a known collection of functions on $T$, then $hat{y}(s)$ is a prediction for $Y(s)$ and the function $hat{y}$ is called a prediction function. Mean-estimation functions are defined similarly. For certain prediction problems based on imprecise observations, characterizations are obtained for these functions in terms of the covariance structure of the process. For a particular prediction problem $hat{y}$ is shown to be a spline function interpolating a convex set." @default.
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- W2023926812 date "1979-07-01" @default.
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- W2023926812 title "Time Series Prediction Functions Based on Imprecise Observations" @default.
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- W2023926812 doi "https://doi.org/10.1214/aos/1176344730" @default.
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