document: Non-asymptotic confidence ellipsoids for the least-squares estimate We consider the finite sample properties of least-squares system identification , and derive non-asymptotic confidence ellipsoids for the estimate . The shape of the confidence ellipsoids is similar to the shape of the ellipsoids derived using asymptotic theory , but unlike asymptotic theory , they are valid for a finite number of data points . The probability that the estimate belongs to a certain ellipsoid has a natural dependence on the volume of the ellipsoid , the data generating mechanism , the model order and the number of data points available
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