Academic

Abstract

In this talk, we are going to discuss nonparametric methods to tackle two types of quantile regression problems that are frequently encountered in real-life applications. First, we consider time series observations where the covariate vector is repeated many times for different values of the response. Such data abounds in climate studies. We propose a model-free nonparametric estimator of conditional quantile in this setting, improving on the restrictive structure of conventional approaches. Relevant asymptotic theories are derived under a very general framework. Through a simulation study, we show that the predictive accuracy of the proposed method is remarkably high compared to other approaches, especially for higher quantiles. The usefulness of the proposed method is then illustrated with well-known tropical cyclone wind-speed data.  

In the second part of the talk, we will focus on the quantile regression problems in spatio-temporal data, which appears in many economic and environmental applications. Building on the above-mentioned work, here we develop a nonparametric technique that requires minimal assumptions and can be used even when explicit information on the locations is not available. Detailed asymptotic theory of our method is then derived. We also show the usefulness of the method through an extensive simulation study. Finally, a real-life application of electricity demand forecasting is carried out.