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On adaptive estimation in partial linear models

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  • Golubev, Georgi
  • Härdle, Wolfgang

Abstract

The problem of estimation of the finite dimensional parameter in a partial linear model is considered. We derive upper and lower bounds for the second minimax order risk and show that the second order minimax estimator is a penalized maximum likelihood estimator. It is well known that the performance of the estimator is depending on the choice of a smoothing parameter. We propose a practically feasible adaptive procedure for the penalization choice.

Suggested Citation

  • Golubev, Georgi & Härdle, Wolfgang, 1997. "On adaptive estimation in partial linear models," SFB 373 Discussion Papers 1997,100, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:1997100
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    References listed on IDEAS

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    1. Hardle, W. & Nussbaum, M., 1990. "Kernel estimation: the equivalent spline smoothing method," LIDAM Discussion Papers CORE 1990013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    3. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
    4. Härdle, W.K. & Mammen, E. & Müller, M.D., 1996. "Testing Parametric versus Semiparametric Modelling in Generalized Linear Models," Other publications TiSEM 3b9b6d39-869e-4ecd-9982-6, Tilburg University, School of Economics and Management.
    5. Härdle, W.K. & Mammen, E. & Müller, M.D., 1996. "Testing Parametric versus Semiparametric Modelling in Generalized Linear Models," Discussion Paper 1996-42, Tilburg University, Center for Economic Research.
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