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Spatial aggregation of local likelihood estimates with applications to classification

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  • Belomestny, Denis
  • Spokoiny, Vladimir

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 the method 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

  • Belomestny, Denis & Spokoiny, Vladimir, 2006. "Spatial aggregation of local likelihood estimates with applications to classification," SFB 649 Discussion Papers 2006-036, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2006-036
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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.
    2. J. Fan & M. Farmen & I. Gijbels, 1998. "Local maximum likelihood estimation and inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 591-608.
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