Semiparametric model averaging for high dimensional conditional quantile prediction
Abstract
In this article, we propose a penalized high dimensional semiparametric model average quantile prediction approach that is robust for forecasting the conditional quantile of the response. We consider a two-step estimation procedure. In the first step, we use a local linear regression approach to estimate the individual marginal quantile functions, and approximate the conditional quantile of the response by an affine combination of one-dimensional marginal quantile regression functions. In the second step, based on the nonparametric kernel estimates of the marginal quantile regression functions, we utilize a penalized method to estimate the suitable model weights vector involved in the approximation. The objective of the second step is to select significant variables whose marginal quantile functions make a significant contribution to estimating the joint multivariate conditional quantile function. Under some mild conditions, we have established the asymptotic properties of the proposed robust estimator. Finally, simulations and a real data analysis have been used to illustrate the proposed method.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2018
- DOI:
- 10.48550/arXiv.1809.01364
- arXiv:
- arXiv:1809.01364
- Bibcode:
- 2018arXiv180901364T
- Keywords:
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- Mathematics - Statistics Theory