Time-variant nonparametric extreme quantile estimation with application to US temperature data

Abstract

Statistical modelling for several years of daily temperature data is somewhat challenging due to remarkable variations of negative and positive temperatures throughout the year. A scatter plot of day and daily temperature shows the high magnitude of variations among data points as dots fall only in the first and fourth quadrants. One parametric modelling approach to this data is to use quantile regression to obtain regression lines on different quantiles. However, these quantile lines cannot make reliable predictions on extreme quantiles when time-variant quantiles differ significantly. In this paper, we develop several two-step nonparametric smoothing estimators and show their superiority over quantile regression for smoothing estimation of nonparametric quantiles with a novel application to temperature data. Narrower bootstrap confidence bands, smaller Minimum Absolute Distance (MAD), smaller bias and MSE, and higher coverage from the application and simulation results show that smoothing curves obtained from these smoothing estimators outperform the quantile regression line.