# Quantile regression and Extreme Value Analysis

Quantile regression and Extreme Value Analysis
Organizer and Chair: Mei Ling Huang (Brock University)
[PDF]

VINCENZO COIA, University of British Columbia
Forecasting Extremes for Flooding  [PDF]

When forecasting using past data, methods such as regression and maximum likelihood are available for reporting a predictive distribution that reflects what a typical outcome might be. However, these techniques are inadequate at structuring and fitting the predictive distribution's tail -- a shortfall when the end-user is only interested in what an extreme outcome might be. To get around these shortcomings, a copula-based nonlinear modelling technique and a composite quantile regression model-fitting technique are proposed. The result is an approach for building the tail of a predictive distribution that addresses questions like how bad could it get?'', and is applied to flood forecasting of the Bow River in Alberta.
KEITH KNIGHT, University of Toronto
Non-parametric Estimation of Extreme Conditional Quantiles and Lawson's Algorithm  [PDF]

Lawson's algorithm, developed in the early 1960s by C.L. Lawson, is an algorithm for computing $L_\infty$ estimates in a linear regression model; it is perhaps the original iteratively reweighted least squares (IRLS) algorithm. We will explore the use of a similar IRLS algorithm to compute non-parametric estimates of extreme (and near-extreme) conditional quantiles.
CHRISTINE NGUYEN, Brock University
On Weighted Quantile Regression  [PDF]

In recent years, studies of heavy tailed distributions have rapidly developed. For multivariate heavy tailed distributions, estimation of conditional quantiles at very high or low tails is of interest in numerous applications. Quantile regression uses an L1- loss function, and the optimal solution of linear programming for estimating coefficients of regression. This paper proposes a weighted quantile regression method on high quantile regression for certain extreme value sets. The Monte Carlo simulations show good results of the proposed weighted method. Comparisons of the proposed method and existing methods are given. The paper also investigates real-world examples by using the proposed weighted method.