A note on unconditional properties of a parametrically guided Nadaraya-Watson estimator. (English) Zbl 0927.62038
Summary: Asymptotic properties of a semiparametric regression estimator proposed by the author [Parametrically guided nonparametric regression. Tech. Rep. No. 18, Depth. Math., Univ. Oslo (1996); see also the preceding review, Zbl 0927.62037] are derived, without conditioning on the predictor variables. The leading terms of unconditional asymptotic bias and variance are equal to those in the expressions obtained conditioned on the design in Glad (1996), while the unconditional approximations derived in this paper are of higher accuracy.
MSC:
| 62G08 | Nonparametric regression and quantile regression |
Keywords:
bias reduction; correction factor; kernel estimators; unconditional properties; semiparametric regressionCitations:
Zbl 0927.62037References:
| [1] | Fan, J., Local linear regression smoothers and their minimax efficiencies, Ann. Statist., 21, 196-216 (1993) · Zbl 0773.62029 |
| [2] | Fan, J.; Gijbels, I., Local Polynomial Modelling and Its Applications (1996), Chapman and Hall: Chapman and Hall London · Zbl 0873.62037 |
| [3] | Glad, I. K., Parametrically guided nonparametric regression, (Technical Report. Technical Report, Scandinavian Journal of Statistics (1996), Department of Mathematics, University of Oslo), to appear · Zbl 0927.62037 |
| [4] | Hjort, N. L.; Glad, I. K., Nonparametric density estimation with a parametric start, Ann. Statist., 23, 882-904 (1995) · Zbl 0838.62027 |
| [5] | Hjort, N. L.; Glad, I. K., On the exact performance of a multiplicative semiparametric density estimator, (Technical Report (1996), Department of Mathematics, University of Oslo), No. 8 1996, Submitted |
| [6] | Ruppert, D.; Wand, M. P., Multivariate locally weighted least squares regression, Ann. Statist., 22, 1346-1370 (1994) · Zbl 0821.62020 |
| [7] | Scott, D. W., Multivariate Density Estimation: Theory, Practice, and Visualization (1992), Wiley: Wiley New York · Zbl 0850.62006 |
| [8] | Seifert, B.; Gasser, T., Finite-sample variance of local polynomials: Analysis and solutions, J. Amer. Statist. Assoc., 91, 267-275 (1996) · Zbl 0871.62042 |
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