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Spatial aggregation of local likelihood estimates with applications to classification

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Author Info
Denis Belomestny
Vladimir Spokoiny

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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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Publisher 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
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Handle: RePEc:hum:wpaper:sfb649dp2006-036

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

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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  1. V. Spokoiny, . "Estimation of a Function with Discontinuities via Local Polynomial Fit with an Adaptive Window Choice," Sonderforschungsbereich 373 1998-1, Humboldt Universitaet Berlin.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Dirk Temme & Lutz Hildebrandt, 2006. "Formative Measurement Models in Covariance Structure Analysis: Specification and Identification," SFB 649 Discussion Papers SFB649DP2006-083, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  2. 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. [Downloadable!]
  3. Christian Stoltenberg, 2006. "Real Balance Effects, Timing and Equilibrium Determination," SFB 649 Discussion Papers SFB649DP2006-073, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  4. Taleb Ahmad & Wolfgang Härdle & Julius Mungo, 2006. "On the Difficulty to Design Arabic E-learning System in Statistics," SFB 649 Discussion Papers SFB649DP2006-062, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  5. Kai Detlefsen & Wolfgang Härdle, 2006. "Forecasting the Term Structure of Variance Swaps," SFB 649 Discussion Papers SFB649DP2006-052, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  6. Carsten Trenkler & Pentti Saikkonen & Helmut Lütkepohl, 2006. "Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break," SFB 649 Discussion Papers SFB649DP2006-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  7. Dominique Demougin & Oliver Fabel, 2006. "The Division of Ownership in New Ventures," SFB 649 Discussion Papers SFB649DP2006-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  8. Bruno Deffains & Dominique Demougin, 2006. "Governance: Who Controls Matters," SFB 649 Discussion Papers SFB649DP2006-053, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  9. Dirk Temme & Henning Kreis & Lutz Hildebrandt, 2006. "PLS Path Modeling – A Software Review," SFB 649 Discussion Papers SFB649DP2006-084, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  10. Matthias Paustian & Christian Stoltenberg, 2006. "Optimal Interest Rate Stabilization in a Basic Sticky-Price Model," SFB 649 Discussion Papers SFB649DP2006-072, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  11. Jenny Kragl & Julia Schmid, 2006. "Relational Contracts and Inequity Aversion," SFB 649 Discussion Papers SFB649DP2006-085, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  12. Enzo Giacomini & Wolfgang Härdle & Ekaterina Ignatieva & Vladimir Spokoiny, 2006. "Inhomogeneous Dependency Modelling with Time Varying Copulae," SFB 649 Discussion Papers SFB649DP2006-075, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  13. Szymon Borak & Wolfgang Härdle & Stefan Trück & Rafal Weron, 2006. "Convenience Yields for CO2 Emission Allowance Futures Contracts," SFB 649 Discussion Papers SFB649DP2006-076, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  14. Tim Grebe & Julia Schmid & Andreas Stiehler, 2006. "Do Individuals Recognize Cascade Behavior of Others? - An Experimental Study -," SFB 649 Discussion Papers SFB649DP2006-079, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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