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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

    as
    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. Ying Chen & Bo Li, 2017. "An Adaptive Functional Autoregressive Forecast Model to Predict Electricity Price Curves," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(3), pages 371-388, July.
    3. Ying Chen & Wolfgang Härdle & Uta Pigorsch, 2009. "Localized Realized Volatility Modelling," SFB 649 Discussion Papers SFB649DP2009-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Denis Belomestny & Grigori Milstein & Vladimir Spokoiny, 2009. "Regression methods in pricing American and Bermudan options using consumption processes," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 315-327.
    5. Ying Chen & Wolfgang Härdle & Vladimir Spokoiny, 2006. "GHICA - Risk Analysis with GH Distributions and Independent Components," SFB 649 Discussion Papers SFB649DP2006-078, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. 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.

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    More about this item

    Keywords

    adaptive weights; local likelihood; exponential family; classification;
    All these keywords.

    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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