Summary: For . and i integer between 1 and n, let be fixed design points in a compact subset S of , , and let be observations taken at these points through g, an unknown continuous real-valued function defined on , and subject to errors ; that is, . For any x in , g(x) is estimated by
where and are suitable weights. If the errors 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 , , are coming from a strictly stationary sequence obeying any one of the four standard modes of mixing.