Consistent regression estimation with fixed design points under dependence conditions

George G. Roussas

Statistics & Probability Letters, 1989, vol. 8, issue 1, 41-50

Abstract: For n = 1, 2,... and i integer between 1 and n, let xni be fixed design points in a compact subset S of , and let Yni be observations taken at these points through g, an unknown continuous real-valued function defined on , and subject to errors [var epsilon]ni; that is, Yni = g(xni) + [var epsilon]ni. For any x in , g(x) is estimated by gn(x; xn) = [Sigma]ni = 1wni(x; xn)Yni, where xn = (xn1,...,xnn) and wni(·;·) are suitable weights. If the errors [var epsilon]ni are centered at their expectations, the proposed estimate is asymptotically unbiased. It is also consistent in quadratic mean and strongly consistent, if, in addition and for each n, the random variables [var epsilon]ni, i [greater-or-equal, slanted] 1, are coming from a strictly stationary sequence obeying any one of the four standard modes of mixing.

Keywords: nonparametric; estimation; regression; estimation; stationarity; mixing; asymptotic; unbiasedness; consistency; in; quadratic; mean; strong; consistency (search for similar items in EconPapers)
Date: 1989
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Citations: View citations in EconPapers (23)

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