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Title: Quantile regression for longitudinal data: A convex clustering approach Authors:  Stanislav Volgushev - University of Toronto (Canada)
Jiaying Gu - University of Toronto (Canada) [presenting]
Abstract: A penalization-based approach is proposed to automatic discovery of group structure in quantile regression with panel data. More precisely, we assume that the observed individuals come from a population with an unknown number of types and each type is allowed to have its own coefficients in a linear quantile regression model. In contrast to existing literature, the number of types in the population does not need to be specified in advance. Rather, a merit of the proposed penalization-based approach is that the number of types and group membership is determined in a data-driven fashion. An adaptive method for finding the tuning parameter is also proposed. Consistency of the procedure for estimating group membership as well as asymptotic normality of the resulting quantile regression coefficients within each group are established.