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- W2019095613 abstract "mean of a random scalar Y conditional on a random vector X E Rd. Let H(x) E(YIX = x) denote the conditional mean function. This paper is concerned with estimating H under weak assumptions about its functional form when X is a multidimensional, continuous random variable. The paper describes a model that nests single-index, additive, and multiplicative models and that can be estimated with a faster rate of convergence in probability than can a fully nonparametric model. Nonparametric estimation of H is usually unattractive when X is multidimensional. The rate of convergence of nonparametric estimators decreases rapidly as the dimension of X increases, and nonparametric estimates can be very imprecise with samples of practical size when X is multidimensional (the curse of dimensionality). This problem can be overcome through the use of dimension-reduction methods. They reduce the effective dimension of the estimation problem by making assumptions about the functional form of H that are stronger than those of a fully nonparametric estimator but weaker than those of a finite-dimensional parametric model. One method of dimension reduction is semiparametric single-index modeling. The best known and most easily estimated semiparametric single-index model assumes that (1.1) H(x) = G( 3'x), where ,3 is an unknown d x 1 vector and G is an unknown function. The vector /3 can be estimated with an n - 1/2 rate of convergence in probability, which is the rate that would be obtained if G were known (Han (1987), Hardle and Stoker (1989), Horowitz and Hardle (1996), Ichimura (1993), Klein and Spady (1993), Newey and Stoker (1993), Powell, Stock, and Stoker (1989), Sherman (1993), Stoker (1991)). G can be estimated with the rate of convergence n -r/(2r+ 1), where r is an integer that depends on the smoothness of G but not on d. Dimension reduction can also be achieved by using a nonparametric generalized additive model. In such a model," @default.
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- W2019095613 date "2001-03-01" @default.
- W2019095613 modified "2023-09-28" @default.
- W2019095613 title "Nonparametric Estimation of a Generalized Additive Model With an Unknown Link Function" @default.
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- W2019095613 doi "https://doi.org/10.1111/1468-0262.00200" @default.
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