VARYING DEGREE POLYNOMIAL REGRESSION * I . RATES OF CONVERGENCE ( Abbreviated Title : VARYING DEGREE POLYNOMIAL REGRESSION
نویسنده
چکیده
For a regression model Yt = gO(x t) + e t , the unknown function gO is estimated consistently using varying degree polynomial regression. Consistency is with respect to a class of norms similar to weighted Sobolev norms, and the method of proof involves metric entropy calculations that enable the development of rates of convergence in these norms. The estimator is viewed as the solution to some-member of a wide class of optimization problems, including those associated with least squares, maximum likelihood, and M-estimators; an M-estimator is used to illustrate the main results. Asymptotic normality is shown in a subsequent paper.
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