Some linear models are necessarily parametric

Abram Kagan and Lawrence A. Shepp

Statistics & Probability Letters, 1998, vol. 37, issue 1, 77-80

Abstract: We prove the surprising result that rather general assumptions on the set of admissible signals [xi](t) observed in the presence of additive noise [var epsilon](t) on a closed interval [a, b], imply that the set is finite dimensional, i.e., [xi](t) = [theta]1[xi]1(t) + ... + [theta]m[xi]m(t) for some integer m [greater-or-equal, slanted] 1 and fixed functions [xi]1(t),..., [xi]m(t). Thus, estimating the signal [xi](t) from observations of x(t) = [xi](t) + [var epsilon](t) reduces to estimating the parameters [theta]1,...,[theta]m. This gives a strong argument in favor of parametric linear models.

Keywords: Linear; models; L2-theory (search for similar items in EconPapers)
Date: 1998
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