Smoothness Adaptive AverageDerivative Estimation
AbstractMany important models, such as index models widely used in limiteddependent variables, partial linear models and nonparametric demand studiesutilize estimation of average derivatives (sometimes weighted) of theconditional mean function. Asymptotic results in the literature focus onsituations where the ADE converges at parametric rates (as a result ofaveraging); this requires making stringent assumptions on smoothness of theunderlying density; in practice such assumptions may be violated. We extendthe existing theory by relaxing smoothness assumptions. We consider boththe possibility of lack of smoothness and lack of precise knowledge of degreeof smoothness and propose an estimation strategy that produces the bestpossible rate without a priori knowledge of degree of density smoothness. Thenew combined estimator is a linear combination of estimators correspondingto different bandwidth/kernel choices that minimizes the trace of the part ofthe estimated asymptotic mean squared error that depends on the bandwidth.Estimation of the components of the AMSE, of the optimal bandwidths,selection of the set of bandwidths and kernels are discussed. Monte Carloresults for density weighted ADE confirm good performance of the combinedestimator.
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Bibliographic InfoPaper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2008/529.
Date of creation: Aug 2008
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Nonparametric estimation; density weighted average derivativeestimator; combined estimator.;
Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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- Wolfgang Härdle & Werner Hildenbrand & Michael Jerison, 1989.
"Empirical Evidence on the Law of Demand,"
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- Haerdle,W. Hildenbrand,W. Jerison,M., 1988. "Empirical evidence on the law of demand," Discussion Paper Serie A 193, University of Bonn, Germany.
- HARDLE, Wolfgang & HILDENBRAND, Werner & JERISON, Michael, . "Empirical evidence on the law of demand," CORE Discussion Papers RP -968, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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