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Spatial aggregation of local likelihood estimates with applications to classification

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  • 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.

Suggested Citation

  • Denis Belomestny & Vladimir Spokoiny, 2006. "Spatial aggregation of local likelihood estimates with applications to classification," SFB 649 Discussion Papers SFB649DP2006-036, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2006-036
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-036.pdf
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    References listed on IDEAS

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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.
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    Cited by:

    1. Mstislav Elagin, 2008. "Locally adaptive estimation methods with application to univariate time series," Papers 0812.0449, arXiv.org.
    2. Chen, Ying & Härdle, Wolfgang Karl & Pigorsch, Uta, 2010. "Localized Realized Volatility Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1376-1393.
    3. Chen, Ying & Härdle, Wolfgang & Spokoiny, Vladimir, 2010. "GHICA -- Risk analysis with GH distributions and independent components," Journal of Empirical Finance, Elsevier, vol. 17(2), pages 255-269, March.
    4. Dedy Dwi Prastyo & Wolfgang Karl Härdle, 2014. "Localising Forward Intensities for Multiperiod Corporate Default," SFB 649 Discussion Papers SFB649DP2014-040, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    adaptive weights; local likelihood; exponential family; classification;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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