## Additive models for quantile regression: model selection and confidence bands.(English)Zbl 1236.62031

Summary: Additive models for conditional quantile functions provide an attractive framework for nonparametric regression applications focusing on the features of the response beyond its central tendency. Total variation roughness penalities can be used to control the smoothness of the additive components much as squared Sobelev penalties are used for classical $$L_{2}$$ smoothing splines. We describe a general approach to estimation and inference for additive models of this type. We focus attention primarily on the selection of the smoothing parameters and on the construction of confidence bands for the nonparametric components. Both pointwise and uniform confidence bands are introduced; the uniform bands are based on the H. Hotelling [Am. J. Math. 61, 440–460 (1939: Zbl 0020.38302)] tube approach. Some simulation evidence is presented to evaluate finite sample performance and the methods are also illustrated with an application to modeling childhood malnutrition in India.

### MSC:

 62G08 Nonparametric regression and quantile regression 62G15 Nonparametric tolerance and confidence regions 65C60 Computational problems in statistics (MSC2010)

### Keywords:

confidence bands; Hotelling tubes

Zbl 0020.38302

### Software:

ConfBands; quantreg; mgcv; gamair; SemiPar
Full Text:

### References:

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