Local likelihood modelling via stagewise aggregation
- Belomestny, Denis
- Spokoiny, Vladimir
2010 Mathematics Subject Classification
- 62G05 62G07 62G08 62H30
- aggregation, local likelihood, exponential family, density estimation, classification, spatial adaptivity
The paper presents a unified approach to local likelihood estimation for a broad class of nonparametric models, including e.g. the regression, density, Poisson and binary response model. Given a sequence of local likelihood estimates which we call "weak" estimates, the proposed method yields a new aggregated estimate whose pointwise risk does not exceed the smallest risk among all "weak" estimates multiplied by some logarithmic factor. We establish a number of important theoretical results concerning optimality of the aggregated estimate and show a good performance of the procedure in simulated examples.
- Ann. Statist., 25 (2007) pp. 2287--2311.