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Spatial aggregation of local likelihood estimates with applications to classification

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Author Info

  • Denis Belomestny
  • Vladimir Spokoiny

Abstract

This paper presents a new method for spatially adaptive local likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of themethod is given a sequence of local likelihood estimates (``weak´´ estimates),to construct a new aggregated estimate whose pointwise risk is of order of the smallest risk among all ``weak´´ estimates. We also propose a new approach towards selecting the parameters of the procedure by providing the prescribed behavior of the resulting estimate in the simple parametric situation. We establish a number of important theoretical results concerning the optimality of the aggregated estimate. In particular, our ``oracle´´ results claims that its risk is up to some logarithmic multiplier equal to the smallest risk for the given family of estimates. The performance of the procedure is illustrated by application to the classification problem. A numerical study demonstrates its nice performance in simulated and real life examples.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-036.

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Length: 33 pages
Date of creation: Apr 2006
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2006-036

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Keywords: adaptive weights; local likelihood; exponential family; classification;

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References

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  1. Spokoiny, Vladimir G., 1998. "Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice," SFB 373 Discussion Papers 1998,1, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. repec:wop:humbsf:1998-1 is not listed on IDEAS
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Cited by:
  1. Chen, Ying & Härdle, Wolfgang & Spokoiny, Vladimir, 2010. "GHICA -- Risk analysis with GH distributions and independent components," Journal of Empirical Finance, Elsevier, Elsevier, vol. 17(2), pages 255-269, March.
  2. Ying Chen & Wolfgang Härdle & Uta Pigorsch, 2009. "Localized Realized Volatility Modelling," SFB 649 Discussion Papers SFB649DP2009-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Mstislav Elagin, 2008. "Locally adaptive estimation methods with application to univariate time series," Papers 0812.0449, arXiv.org.

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