The laws of the iterated logarithm of some estimates in partly linear models
AbstractConsider the regression model Yi = xi'[beta] + g(ti) + ei, 1 [less-than-or-equals, slant] i [less-than-or-equals, slant] n, where xi = (xi1, xi2, ..., xip)' and ti (ti [epsilon] [0, 1]) are known and nonrandom design points, [beta] = ([beta]1, ..., [beta]p)' (p [greater-or-equal, slanted] 1) is an unknown parameter, g(Â·) is an unknown function, and ei are i.i.d. random errors. Based on g estimated by nonparametric kernel estimation, the laws of the iterated logarithm of the least-square estimator of [beta] and an estimator of [sigma]2 = Ee12
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 25 (1995)
Issue (Month): 2 (November)
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